Question

What is the chain rule?

Answer 1

Chain Rule:

If $f$ and $g$are the differentiable functions and $F$ is a composite function defined by $F\left(x\right)=f\left(g\left(x\right)\right)$, then $F$ is a differentiable function and $F\text{'}$ is given by

$F\text{'}\left(x\right)=f\text{'}\left(g\left(x\right)\right)·g\text{'}\left(x\right)$

If $y=f\left(u\right)$ and $u=g\left(x\right)$ are both differentiable functions, then

$\frac{dy}{dx}=\frac{dy}{du}·\frac{du}{dx}$