What is derivative of $sin ax$ where $a$ is a constant?











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1
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What is the derivative of $sin a x$ where $a$ is a constant.




Actually, I'm studying Physics and not so well-versed with calculus. So, I have studied the basic rules of calculus but am stuck here.



I somewhat know about the product rule but don't get what to do if a constant is given in a trigonometric function, be it $sin ax $ or $cos ax$. Whatever..
Please help me get my concept clear.




Thank You!






calculus algebra-precalculus derivatives differential







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  • 1




    Apply the chain rule.
    – user3482749
    2 days ago















up vote
1
down vote

favorite












What is the derivative of $sin a x$ where $a$ is a constant.




Actually, I'm studying Physics and not so well-versed with calculus. So, I have studied the basic rules of calculus but am stuck here.



I somewhat know about the product rule but don't get what to do if a constant is given in a trigonometric function, be it $sin ax $ or $cos ax$. Whatever..
Please help me get my concept clear.




Thank You!






calculus algebra-precalculus derivatives differential







share|cite|improve this question









New contributor




Chaku Daku is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
















  • 1




    Apply the chain rule.
    – user3482749
    2 days ago













up vote
1
down vote

favorite









up vote
1
down vote

favorite











What is the derivative of $sin a x$ where $a$ is a constant.




Actually, I'm studying Physics and not so well-versed with calculus. So, I have studied the basic rules of calculus but am stuck here.



I somewhat know about the product rule but don't get what to do if a constant is given in a trigonometric function, be it $sin ax $ or $cos ax$. Whatever..
Please help me get my concept clear.




Thank You!






calculus algebra-precalculus derivatives differential







share|cite|improve this question









New contributor




Chaku Daku is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











What is the derivative of $sin a x$ where $a$ is a constant.




Actually, I'm studying Physics and not so well-versed with calculus. So, I have studied the basic rules of calculus but am stuck here.



I somewhat know about the product rule but don't get what to do if a constant is given in a trigonometric function, be it $sin ax $ or $cos ax$. Whatever..
Please help me get my concept clear.




Thank You!






calculus algebra-precalculus derivatives differential




calculus algebra-precalculus derivatives differential






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Chaku Daku is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited 2 days ago









Asaf Karagila♦

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  • 1




    Apply the chain rule.
    – user3482749
    2 days ago














  • 1




    Apply the chain rule.
    – user3482749
    2 days ago








1




1




Apply the chain rule.
– user3482749
2 days ago




Apply the chain rule.
– user3482749
2 days ago










3 Answers
3






active

oldest

votes

















up vote
6
down vote













HINT



Recall that by chain rule



$$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$






share|cite|improve this answer




























    up vote
    3
    down vote













    begin{array}{c}
    frac{d}{{dx}}left( {sin ax} right) = left( {cos ax} right)frac{d}{{dx}}left( {ax} right)\
    = left( {cos ax} right) cdot a cdot frac{{dx}}{{dx}}\
    = left( {cos ax} right) cdot a cdot 1\
    = aleft( {cos ax} right)
    end{array}






    share|cite|improve this answer

















    • 1




      Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
      – Chris
      2 days ago






    • 1




      @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
      – Paul Sinclair
      2 days ago


















    up vote
    1
    down vote













    Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.






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      Your Answer





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      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes








      up vote
      6
      down vote













      HINT



      Recall that by chain rule



      $$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$






      share|cite|improve this answer

























        up vote
        6
        down vote













        HINT



        Recall that by chain rule



        $$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$






        share|cite|improve this answer























          up vote
          6
          down vote










          up vote
          6
          down vote









          HINT



          Recall that by chain rule



          $$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$






          share|cite|improve this answer












          HINT



          Recall that by chain rule



          $$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 2 days ago









          gimusi

          88.8k74394




          88.8k74394






















              up vote
              3
              down vote













              begin{array}{c}
              frac{d}{{dx}}left( {sin ax} right) = left( {cos ax} right)frac{d}{{dx}}left( {ax} right)\
              = left( {cos ax} right) cdot a cdot frac{{dx}}{{dx}}\
              = left( {cos ax} right) cdot a cdot 1\
              = aleft( {cos ax} right)
              end{array}






              share|cite|improve this answer

















              • 1




                Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
                – Chris
                2 days ago






              • 1




                @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
                – Paul Sinclair
                2 days ago















              up vote
              3
              down vote













              begin{array}{c}
              frac{d}{{dx}}left( {sin ax} right) = left( {cos ax} right)frac{d}{{dx}}left( {ax} right)\
              = left( {cos ax} right) cdot a cdot frac{{dx}}{{dx}}\
              = left( {cos ax} right) cdot a cdot 1\
              = aleft( {cos ax} right)
              end{array}






              share|cite|improve this answer

















              • 1




                Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
                – Chris
                2 days ago






              • 1




                @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
                – Paul Sinclair
                2 days ago













              up vote
              3
              down vote










              up vote
              3
              down vote









              begin{array}{c}
              frac{d}{{dx}}left( {sin ax} right) = left( {cos ax} right)frac{d}{{dx}}left( {ax} right)\
              = left( {cos ax} right) cdot a cdot frac{{dx}}{{dx}}\
              = left( {cos ax} right) cdot a cdot 1\
              = aleft( {cos ax} right)
              end{array}






              share|cite|improve this answer












              begin{array}{c}
              frac{d}{{dx}}left( {sin ax} right) = left( {cos ax} right)frac{d}{{dx}}left( {ax} right)\
              = left( {cos ax} right) cdot a cdot frac{{dx}}{{dx}}\
              = left( {cos ax} right) cdot a cdot 1\
              = aleft( {cos ax} right)
              end{array}







              share|cite|improve this answer












              share|cite|improve this answer



              share|cite|improve this answer










              answered 2 days ago









              Krishna Srivastav

              894




              894








              • 1




                Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
                – Chris
                2 days ago






              • 1




                @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
                – Paul Sinclair
                2 days ago














              • 1




                Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
                – Chris
                2 days ago






              • 1




                @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
                – Paul Sinclair
                2 days ago








              1




              1




              Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
              – Chris
              2 days ago




              Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
              – Chris
              2 days ago




              1




              1




              @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
              – Paul Sinclair
              2 days ago




              @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
              – Paul Sinclair
              2 days ago










              up vote
              1
              down vote













              Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.






              share|cite|improve this answer










              New contributor




              Rohit Bharadwaj is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
              Check out our Code of Conduct.






















                up vote
                1
                down vote













                Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.






                share|cite|improve this answer










                New contributor




                Rohit Bharadwaj is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                Check out our Code of Conduct.




















                  up vote
                  1
                  down vote










                  up vote
                  1
                  down vote









                  Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.






                  share|cite|improve this answer










                  New contributor




                  Rohit Bharadwaj is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.









                  Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.







                  share|cite|improve this answer










                  New contributor




                  Rohit Bharadwaj is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.









                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited 2 days ago









                  Tianlalu

                  2,859832




                  2,859832






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                  answered 2 days ago









                  Rohit Bharadwaj

                  518




                  518




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                  New contributor





                  Rohit Bharadwaj is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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                  Rohit Bharadwaj is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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