What is the derivative of this function #y = sin ^ -1 (x^2)?

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Answer 1 · 2017-08-13T02:10:03

$y'(x) = (2x)/(sqrt(1-x^4))$

We're asked to find the derivative

$(dy)/(dx) [sin^-1(x^2)]$

Let's use the chain rule first:

$d/(dx) [sin^-1(x^2)] = d/(du) [sin^-1u] (du)/(dx)$

where

$y'(x) = (d/(dx)[x^2])/(sqrt(1-x^4))$

The derivative of $x^2$ is $2x$ (according to the power rule):

$color(blue)(ulbar(|stackrel(" ")(" "y'(x) = (2x)/(sqrt(1-x^4))" ")|)$