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

Question

1501 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-14T18:11:25

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

Letting $y = arcsin(x^2)$ , then $siny = x^2$ .

Then differentiating both sides with respect to $x$ .

$cosy(dy/dx) = 2x$

$dy/dx = (2x)/cosy$

We know that $cos^2y + sin^2y = 1$ , thus $cosy = sqrt(1 - sin^2y)$ .

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

Recall that $siny = x^2$ , therefore, $sin^2y = x^4$ .

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

Hopefully this helps!

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