Homework Help: How may I derive this equation?

1. May 20, 2009

staka

How may I derive y=cos^3(sinx)?
I thought simply just y=3cos(sinx)^2(cosx)...

Answer given is -3cosxsin(sinx)cos^2(sinx) but no idea how to get to that.

2. May 20, 2009

C.E

I am a bit confused about what the exact question is. What is it?

3. May 20, 2009

staka

How to derive the function: y=cos^3(sinx) is my question... solving for y'=.

4. May 20, 2009

Staff: Mentor

I think you didn't use the chain rule enough times.
You need the derivative of cos3(sin(x)) with respect to cos(sin(x)) times the derivative of cos(sin(x)) wrt sin(x) times the derivative of sin(x) wrt x.

5. May 20, 2009

cristo

Staff Emeritus
By derive you mean differentiate, right?

Try writing t=sinx, then y=[cos(t)]^3. Then, dy/dx=(dy/dt)(dt/dx). Course, you need to use the chain rule again when differentiating y wrt t.

6. May 20, 2009

staka

Alright. I'll retry.. solving.

7. May 20, 2009

C.E

Oh, differentiate now I know what you are trying to do. Are you familiar with the chain rule?

8. May 20, 2009

staka

I am familar with the chain rule.. I'll retry.

9. May 20, 2009

staka

Alright thanks. I've solved it correctly.