Maths

1. If f(x)=ln(x+1)^2x. Find f '(x) and express the answer in terms of natural logarithm.

2. If g(x)=ln(x^(2x)+1). Find g '(2) and express the answer in terms of natural logarithm.

3.Prove that the Product Rule is also true for n is a real number, that is If n is a real number, then d/dx(x^(n))=nx^(n-1).
Hints: Use logarithmic differentiation and consider the cases X>0 and X<0.