Chapter 1.7, Problem 84E

If $f\left(x\right)$ is a function, then $\left(f\circ \right)\left(x\right)=f\left(f\left(x\right)\right)$ is the composition of $f$ with itself. This is called an iterated function, and the composition can be repeated many times. For example, $\left(f\circ f\circ f\right)\left(x\right)=f\left(f\left(f\left(x\right)\right)\right)$. Iterated functions are very useful in many areas, including finance (compound interest is a simple case) and the science (in weather forecasting, for example). For each function, use the Chain Rule to find the derivative.

If $f\left(x\right)=x^2+1,\text{find}\frac{d}{dx}\left[\left(f\circ f\circ f\right)\left(x\right)\right]$.