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 = 2x + 3

Answer 1

y = 2x + 3                                             ...(1)
We have to find the inverse function of y = f(x), i.e x in terms of y.
From (1),
2x = y – 3
∴ x = `(y - 3)/(2)`
∴ x = f^–1(y)
= `(y - 3)/(2)`
∴ `"dx"/"dy" = (1)/(2)"d"/"dy"(y - 3)`
= `(1)/(2)(1 - 0)`
= `(1)/(2)`
∴ `"dy"/"dx" = (1)/(("dx"/"dy")`
= `(1)/((1/2)`
= 2.