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

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Answer 1 · 2016-08-12T12:56:07

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

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

$sin y= e^x$

$cos y \ y' = e^x$

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

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

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

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

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