How do you take the derivative of tan(2x)?

1 Answer
Sep 5, 2015

Using the chain rule tan(2x)=2sec^2(2x)

Explanation:

The chain rule is as follows:

d/dx f(g(x)) = [d/dx f(x)]|_(x=g(x)) * d/dx g(x)

...or, in words,
1) Get the derivative of the outer function, plug in the inner function...
2) ...multiplied by the derivative of the inner function.

In tan(2x), the outer function is tan x and the inner function is 2x.

The derivative of tan x is sec^2 x.
Plug in 2x, and we have sec^2 (2x).

So, after our first step, we have:
d/dx tan(2x)
=sec^2 (2x) * d/dx (2x)

Then, we continue:
d/dx tan(2x)
=sec^2 (2x) * d/dx (2x)

=sec^2 (2x) * (2)

=2sec^2(2x)