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

Question

2128 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-22T16:17:34

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

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.

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