Can you differentiate inverse trig functions implicitly ?

3 years ago

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Genevieve Lebsack

1 Answer

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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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