Question

Differentiate the following with regard to x :

y=x^4 times sin x

Answer 1

Given $y=x^4 sin x$

Using chain rule, $\frac{}{}$ if y= uv

$\frac{dy}{dx} = u\frac{dv}{dx}+v\frac{du}{dx}$

Then,

$\frac{dy}{dx} = x^4\frac{d sinx}{dx}+sinx\frac{dx^4}{dx}$

$\frac{dy}{dx} = x^4 cosx + 4x^3sinx$

$\frac{dy}{dx} = x^3(xcosx+4sinx)$