Question

How do you find the derivative of `cos^2x sinx`?

Answer 1

`"the derivative of y="cos^2 x sin x" is "y^'=-2cos x+3cos^3 x`

Explanation:

`a=cos ^2x`

`b=sin x`

`y=cos^2 x sin x`

`y=a*b`

`y^'=a^'*b+b^'*a`

`a^'=-2cos x*sin x`

`b^'=cos x`

`y^'=-2cos x*sin x* sin x+cos x*cos^2 x`

`y^'=-2cos x*sin^2 x+cos^3 x`

`sin^2 x=1-cos^2 x`

`y^'=-2cos x(1-cos^2 x)+cos^3 x`

`y^'=-2cos x+2cos^3 x+cos^3 x`

`y^'=-2cos x+3cos^3 x`

Answer 2

I would replace `cos^2x` by `1-sin^2x`

Explanation:

`cos^2xsinx = (1-sin^2x)sinx = sinx-sin^3x`

The derivative is `cosx-3sin^2xcosx`.

There are other ways to write the derivative.