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

Question

1235 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-10T19:49:13

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!