Question

How do you differentiate `f(x)=x^2cosx` using the product rule?

Answer 1

`2x cosx-x^2sinx`

Explanation:

u and v are functions of x,
u', v' are the derivatives of those functions
(uv)' is the derivative of the product.

The rule for products is (uv)'= u' v+ v'u

The first derivative of `x^2` is `2x`
The first derivative of `cosx` is `-sinx`

So (`x^2 cosx`)'= `2xcosx-sinx x^2`
Or `2x cos x-x^2sinx`