Question

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

Answer 1

`(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`