How do you differentiate f(x)=tan(5x)?

1 Answer
Nov 7, 2016

f'(x)=5sec^2(5x)

Explanation:

Since the function is composed of a function in terms of another function, chain rule must be applied. The two functions are tan(5x), which is in terms of 5x, and 5x which is in terms of x.

f'(x)=(dy)/(du)*(du)/(dx)

Let u=5x

(dy)/(du)=d/(du)tan(u)=sec^2(u)

(du)/(dx)=d/(dx)5x=5

:.f'(x)=5*sec^2(u)=5*sec^2(5x)

=5sec^2(5x)