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