How do you find the derivative of f(x)=3arcsin(x2)?

1 Answer
Feb 20, 2017

dydx=6x1x4

Explanation:

Let y=f(x)

y=3arcsin(x2)

This suggests that sin(y3)=x2

Taking the derivative of both sides, we get:

13cos(y3)dydx=2x

Rearranging and cleaning it up, we get:

dydx=6xcos(y3)

We now need to rewrite cos(y3) in terms of x. We can do this using sin2A+cos2A=1

cos2(y3)+sin2(y3)=1 where sin2(y3)=x4

cos2(y3)=1x4

cos(y3)=1x4

dydx=6x1x4