Here's an example of the chain rule. Suppose we want to calculate:
So we have:
and so:
Therefore the final result is:

$dxde_{2}x $

$f(x)=e_{x}g(x)=2x$

$f_{′}(x)=e_{x}g_{′}(x)=2$

$f_{′}(g(x))g_{′}(x)=e_{2x}2=2e_{2x}$

Here's an example of the chain rule. Suppose we want to calculate:
So we have:
and so:
Therefore the final result is:

$dxde_{2}x $

$f(x)=e_{x}g(x)=2x$

$f_{′}(x)=e_{x}g_{′}(x)=2$

$f_{′}(g(x))g_{′}(x)=e_{2x}2=2e_{2x}$