What is the derivative of this function #y=sin^-1(e^x)#?

Question

20148 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-12T12:56:07

# \ y' =(e^x)/sqrt(1 - e^(2x))#

#y=sin^-1(e^x)#

#sin y= e^x#

#cos y \ y' = e^x#

# \ y' =(e^x)/cos y#

# \ y' =(e^x)/sqrt(1 - sin^2 x)#

# \ y' =(e^x)/sqrt(1 - (e^x)^2)#

# \ y' =(e^x)/sqrt(1 - e^(2x))#