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Question
Find the derivative of the function y = f(x) using the derivative of the inverse function x = f–1(y) in the following:
y = `sqrt(x)`
Solution
y = `sqrt(x)` ...(1)
We have to find the inverse function of y = f(x), i.e. x in terms of y.
From (1), we have
y2 = x
∴ x = y2
∴ x = f–1(y) = y2
∴ `(dx)/(dy) = d/(dy)(y^2)` = 2y
= `2sqrt(x)` ...[By (1)]
∴ `(dy)/(dx) = (1)/((dx/dy)`
= `(1)/(2sqrt(x)`.
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