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!
