Question

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

Answer 1

`2sec^2(2x)`

Explanation:

Assuming that you know the derivative rule: `d/dx(tanx)=sec^2(x)`
`d/dx(tan(2x))` will simply be `sec^2(2x)* d/dx(2x)` according to the chain rule.
Then `d/dx(tan(2x))=2sec^2(2x)`
If you want to easily understand chain rule, just remember my tips: take the normal derivative of the outside (ignoring whatever is inside the parenthesis) and then multiply it by the derivative of the inside (stuff inside the parenthesis)

Answer 2

`2sec^2(2x)`

Explanation:

The first thing to realize is that we're dealing with a composite function `f(g(x))`, where

`f(x)=tanx` and `g(x)=2x`

When we differentiate a composite function, we use the Chain Rule

`f'(g(x))*g'(x)`

From the definition of tangent and an application of the Quotient Rule, we know that `f'(x)=sec^2x`.

We also know that `g'(x)=2`. Now, we have everything we need to plug into the Chain Rule:

`sec^2(2x)*2`, which can be rewritten as

`2sec^2(2x)`

Hope this helps!