Question

How do you differentiate `g(y) =(x^2 + 1)^5sqrtx` using the product rule?

Answer 1

`g'(x)=10x(x^2+1)^4sqrt(x)+1/2*(x+1)^5/sqrt(x)`

Explanation:

Ater the product rule

`(uv)'=u'v+uv'`
and the chain rule

`(f(g(x))'=f'(g(x)g'(x)`
we get

`g'(x)=5(x^2+1)^4*2x*sqrt(x)+(x^2+1)^5*1/2x^(-1/2)`
simplifying we obtain

`((1+x^2)^4(1+21x^2))/(2*sqrt(x))`