Question

derivative of arctan(sinh2x)

Answer 1

first.. do you know the derivative of arctan u?

Answer 2

du over 1 - u^2

Answer 3

switch your sign, then you're right :)

Answer 4

and du is for integration... so it's actually 1 over 1+u^2

Answer 5

1 - u^2 to u^2 - 1?

Answer 6

1 - u^2 into u^2 + 1

Answer 7

should be + not -

Answer 8

\[y= \arctan u\]
\[\tan y = u\]
\[\sec^2 y y' = 1\]
\[y' = \frac{1}{\sec^2 y}\]
\[y' = \frac{1}{u^2 + 1}\]
here's some visuals