How do you find the derivative of $arcsin(x^2)$ ?

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Answer 1 · 2016-11-22T02:15:23

$d/dx arcsin(x^2)= (2x)/sqrt(1 -x^4)$

Let $y = arcsin(x^2) => siny = x^2$

Differentiating wrt x;

$cosydy/dx = 2x$

Using the identity $sin^2A+cos^2A -= 1$

$sin^2y + cos^2y = 1$
$:. (x^2)^2 + cos^2y = 1$
$:. cos^2y = 1 -x^4$
$:. cosy = sqrt(1 -x^4)$

And so;

$sqrt(1 -x^4)dy/dx = 2x$
$:. dy/dx = (2x)/sqrt(1 -x^4)$

How do you find the derivative of arcsin(x^2)arcsin(x^2)?