Derivative Question: Why is dy/dx for cos(2x) not -sin(2x)?

[Miike012]

Example Problem: Finding dy/dx for cos(2x).

knowing that the derivative of cos(x) is -sin(x)...

thus my thought is... when differentiating cos(2x)... why is the derivative not -sin(2x)?

I wasn't aware that I would have to treat that as a composite function...

 

[SteamKing]

Have you learned the chain rule yet?

 

[Miike012]

Yes I have... But I thought I didn't think I had to use the chain rule on this function.

 

[McAfee]

Example Problem: Finding dy/dx for cos(2x).

knowing that the derivative of cos(x) is -sin(x)...

thus my thought is... when differentiating cos(2x)... why is the derivative not -sin(2x)?

I wasn't aware that I would have to treat that as a composite function...

You have to use the chain rule. You are right in which cos(x) is -sin(x) but you also have 2x which the derivative is 2 so the final answer is -2sin(x)

Hope it make things more clear for you.

 

[Mark44]

You have to use the chain rule. You are right in which cos(x) is -sin(x)

No, cos(x) IS NOT -sin(x), but d/dx(cos(x)) = -sin(x).

but you also have 2x which the derivative is 2 so the final answer is -2sin(x)

Hope it make things more clear for you.

 

[McAfee]

No, cos(x) IS NOT -sin(x), but d/dx(cos(x)) = -sin(x).

You knew what I meant. :D

 

[Mark44]

You knew what I meant. :D

Yes, I knew what you meant, so you should work a little harder to say what you mean.