Inner Function Identification

Question

I have having an issue identifying the inner function of this function:

$$f(g(x))=\frac{1}{\sqrt{x+1}}$$

I "need" to take the derivative of it; hence I have to identify the inner function. My current thinking is that the inner function is $\sqrt{x+1}$, and outer would be $\frac{1}{x}$.

Outer

$$\frac{1}{x}$$

Inner

$$\sqrt{x+1}$$

Is my answer to the identification of the outside and inner functions correct?

Answer 1

Those are two possible solutions for the inner and outer functions, however, if you are to apply the chain rule, I would suggest just using $(x+1)^\frac{-1}{2}$ for your chain rule