Question

How do I find the derivative of `y=arcsin(e^x)`?

Answer 1

`(e^x)/(sqrt(1-e^(2x))`

Explanation:

Know that `d/dx[arcsin(u)]=(u')/(sqrt(1-u^2)`.

`y'=(d/dx[e^x])/(sqrt(1-(e^x)^2))=(e^x)/(sqrt(1-e^(2x))`

If you didn't already know that `d/dx[arcsin(u)]=(u')/(sqrt(1-u^2)` or want to know how to derive it, just tell me and I'll be happy to elaborate.