Help with math please

Question

If g(x)=2ln(x+1) and f is a differentiable function of x, what is equivalent to the derivative of f(g(x)) with respect to x?

let f be a differentiable function. if h(x) = (2+f(sinx))^3, what's a correct process for finding h'(x)?

Answer 1

The chain rule states that for h(x) = f(g(x)), then h’(x) = f’(g(x)) • g’(x)

For g(x) = 2ln(x+1), g'(x) = 2/(x+1).

Since you don't specify what f(x) is, we can just say that (f(g(x)))' = f '(2ln(x+1))•2/(x+1)

For the second function you don't state what f(x) is either except that it is a function of sinx.

So f '(sinx) = f '(sinx)•(cosx)

So for h(x) = (2+f(sinx))^3, we can say h'(x) = 3(2+f(sinx))²•f '(sinx)•(cosx)