Question

Find the derivative of the inverse of function y = 2x³ – 6x and calculate its value at x = −2

Answer 1

y = 2x³ – 6x

Differentiating w.r.t. x, we get

`("d"y)/("d"x) = "d"/("d"x)(2x^3 - 6x)`

= 2(3x²) – 6

= 6x² – 6

= 6(x² – 1)

∴ `(("d"y)/("d"x))_(x = -2) = 6[(-2)^2 - 1]`

= 6(3)

= 18

∴ `(("d"x)/("d"y))_(x = -2) = 1/(("d"y)/("d"x))_(x = -2)`

= `1/18`