Question

How do you differentiate `f(x)=(x^2)(x^3+4)` using the product rule?

Answer 1

Use the product rule of differentiation to eventually obtain `5x^4+8x`

Explanation:

According to the product rule, `d/dx[f(x)*g(x)]=f(x)*g'(x)+g(x)*f'(x)`

So applying it in this case we get

`d/dx[(x^2)(x^3+4)]=x^2*3x^2+(x^3+4)*2x`

`=5x^4+8x`