Question

What is the derivative of `tan^2 (e^x)`?

Answer 1

`2e^x tan(e^x)sec^2(e^x)`

Explanation:

Note that `tan^2(e^x) = (tan(e^x))^2`. Then, simply use the chain rule thrice:

`d/dx tan^2(e^x) = d/dx (tan(e^x))^2 = 2 tan(e^x) * sec^2(e^x) * e^x = 2e^x tan(e^x)sec^2(e^x)`