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

Aug 22, 2016

$2 x \cos x - {x}^{2} \sin x$

#### 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 $2 x$
The first derivative of $\cos x$ is $- \sin x$

So (${x}^{2} \cos x$)'= $2 x \cos x - \sin x {x}^{2}$
Or $2 x \cos x - {x}^{2} \sin x$