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

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Answer 1 · 2016-11-10T00:05:01

$d/dx sin^(-1)x = 1/sqrt(1 - x^2)$

Let $y=sin^(-1)x => siny=x$

Differentiating implicitly we have:

$cosydy/dx=1$
$dy/dx=1/cosy$

And using the identity $sin^2y + cos^2y-=1$ we have

$x^2 + cos^2y=1$
$:. cos^2y = 1 - x^2$
$:. cosy = sqrt(1 - x^2)$

Hence, $dy/dx=1/cosy = 1/sqrt(1 - x^2)$

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