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How do you find the derivative of the inverse function #f(x)=sin(arccos t)#?

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Apr 12, 2015

Using trigonometry, rewrite the function.

#f(t)=sin(arccost) # is the sine of an angle in quadrant 1 or 2, whose cosine is #t#.

The sine of such an angle is #sqrt (1-t^2)#.

#f(t) = sqrt (1-t^2)#.

#f'(t)=1/(2sqrt(1-t^2))(-2t) = - t/sqrt (1-t^2)#.

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