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Question

Can you differentiate inverse trig functions implicitly ?

3 years ago

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Genevieve Lebsack


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1 Answer

Liz R Profile Picture
Liz R Verified Sherpa Tutor โœ“

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Yes -this is the method used.


If y=arcsin x then x=siny

Differentiating both sides with respect to x gives


1=cos y (dy/dx).


Rearranging gives dy/dx = 1/cos y.


However cos y = sqrt (1 - sin2y) = sqrt (1- x2) and hence


dy/dx=1/sqrt (1-x2)

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