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

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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))#