Question

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

Answer 1

`g' (x)=(5x^2+16x)/(2 sqrt(x+4)`

Explanation:

Use the formula `d/dx(u v)= u (dv)/dx + v(du)/dx`

Given `g(x)=x^2 sqrt(4+x)`

`g' (x)= x^2*1/(2 sqrt(4+x)) *1+sqrt(4+x)*2x`

`g' (x)=x^2/(2 sqrt(x+4))+2x* sqrt(x+4)*(2 sqrt(x+4))/(2 sqrt(x+4))`

`g' (x)=(x^2+4x^2+16x)/(2 sqrt(x+4))`

`g' (x)=(5x^2+16x)/(2 sqrt(x+4)`