Question

How do you differentiate `y=sec^-1(e^(2x))`?

Answer 1

`2/sqrt{e^{4x}-1}`

Explanation:

`sec y = e^{2x}`

differentiating both sides with respect to `x` :

`sec y tan y {dy}/{dx}=2e^{2x} implies`

`dy/dx = {2 e^{2x}}/{sec y tan y}={2e^{2x}}/{e^{2x}sqrt{(e^{2x})^2-1}}=2/sqrt{e^{4x}-1}`