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

1 Answer
Steve M
Nov 10, 2016

# d/dx sin^(-1)x = 1/sqrt(1 - x^2) #

Explanation:

Let # y=sin^(-1)x => siny=x #

Differentiating implicitly we have:

# cosydy/dx=1 #
# dy/dx=1/cosy #

And using the identity # sin^2y + cos^2y-=1 # we have

# x^2 + cos^2y=1 #
# :. cos^2y = 1 - x^2 #
# :. cosy = sqrt(1 - x^2) #

Hence, # dy/dx=1/cosy = 1/sqrt(1 - x^2) #

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