How do you differentiate f(x)=tan((e^x)^2) using the chain rule?

1 Answer
Jun 29, 2018

(df)/dx=2(e^x)^2sec^2x

Explanation:

(df)/dx=d/dx[tan((e^x)^2)]

Chain rule:
(df)/dx=sec^2xd/dx[(e^x)^2]

Note that (e^x)^2=e^(2x):
(df)/dx=sec^2xd/dx[e^(2x)]
(df)/dx=2e^(2x)sec^2x

Express it in the same fashion as the question:
(df)/dx=2(e^x)^2sec^2x