Question

What is the derivative of this function `sin^3(x)cos(x)`?

Answer 1

Derivative is `3sin^2xcos^2x-sin^4x`

Explanation:

We use the product rule and chain rule here.

Product rule states if `f(x)=g(x)h(x)`, then `(df)/(dx)=(dg)/(dx)xxh(x)+(dh)/(dx)xxg(x)`

and according to chain rule if `y=f(u(x)` then `(dy)/(dx)=(dy)/(du)xx(du)/(dx)`.

Hence as `y=f(x)=sin^3xcosx`

`(df)/(dx)=3sin^2x xx cosx xx cosx+sin^3x xx(-sinx)`

= `3sin^2xcos^2x-sin^4x`