Question

How do you differentiate `f(x)=1/sec(e^(x) )` using the chain rule?

Answer 1

Use trigonometry first, then the derivative of the cosine and the chain rule.

Explanation:

`f(x) = 1/(sec(e^x)) = cos(e^x)`

`f'(x) = -sin(e^x) d/dx(e^x)`

`= -sin(e^x) (e^x)`

`= -e^xsin(e^x)`