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

1 Answer
Jun 12, 2018

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))