# Prove: is y = tan(2x), than y" = 4y . y' ? Thank you!t

##### 1 Answer

Jun 10, 2018

We can compute the first derivative as being

#y' = 2sec^2(2x)#

Now

#4yy' = 4(tan(2x))(2sec^2(2x)) = 8tan(2x)sec^2(2x)#

Therefore this is saying that

#y'' = 8tan(2x)sec^2(2x)#

Let's verify this by differentiating the first derivative.

We can rewrite as

#y' = 2(sec(2x))^2#

#y'' = 2(2sec(2x)sec(2x)tan(2x)(2)#

#y'' = 8sec^2(2x)tan(2x)#

As required. Therefore we've proved the statement.

Hopefully this helps!