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

2 Answers
May 3, 2018

#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)

Aug 12, 2018

#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!