What is derivative of $sin ax$ where $a$ is a constant?
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
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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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add a comment |
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
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
add a comment |
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
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.
Check out our Code of Conduct.
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edited 2 days ago
Asaf Karagila♦
300k32421751
300k32421751
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asked 2 days ago
![](https://i.stack.imgur.com/VKmwV.png?s=32&g=1)
![](https://i.stack.imgur.com/VKmwV.png?s=32&g=1)
Chaku Daku
91
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1
Apply the chain rule.
– user3482749
2 days ago
add a comment |
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
add a comment |
3 Answers
3
active
oldest
votes
up vote
6
down vote
HINT
Recall that by chain rule
$$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$
add a comment |
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}
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
add a comment |
up vote
1
down vote
Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.
New contributor
Rohit Bharadwaj is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
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
$$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$
add a comment |
up vote
6
down vote
HINT
Recall that by chain rule
$$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$
add a comment |
up vote
6
down vote
up vote
6
down vote
HINT
Recall that by chain rule
$$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$
HINT
Recall that by chain rule
$$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$
answered 2 days ago
gimusi
88.8k74394
88.8k74394
add a comment |
add a comment |
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}
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
add a comment |
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}
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
add a comment |
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}
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}
answered 2 days ago
![](https://i.stack.imgur.com/trnaA.png?s=32&g=1)
![](https://i.stack.imgur.com/trnaA.png?s=32&g=1)
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
add a comment |
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
add a comment |
up vote
1
down vote
Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.
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.
add a comment |
up vote
1
down vote
Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.
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.
add a comment |
up vote
1
down vote
up vote
1
down vote
Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.
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.
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.
edited 2 days ago
Tianlalu
2,859832
2,859832
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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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answered 2 days ago
Rohit Bharadwaj
518
518
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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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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.
Rohit Bharadwaj is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
Chaku Daku is a new contributor. Be nice, and check out our Code of Conduct.
Chaku Daku is a new contributor. Be nice, and check out our Code of Conduct.
Chaku Daku is a new contributor. Be nice, and check out our Code of Conduct.
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1
Apply the chain rule.
– user3482749
2 days ago