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) #