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Question
Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them. y = x5 + 2x3 + 3x, at x = 1
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Solution
y = x5 + 2x3 + 3x
Differentiating w.r.t. x, we get
`"dy"/"dx" ="d"/"dx"(x^5 + 2x^3 + 3x)`
= 5x4 + 2 x 3x2 + 3 x 1
= 5x4 + 6x2 + 3
The derivative of inverse function of y = f(x) is given by
`"dx"/"dy" = (1)/(("dy"/"dx")`
= `(1)/(5x^4 + 6x^2 + 3)`
At x = `1, "dx"/"dy"`
= `(1)/(5x^4 + 6x^2 + 3)_(at x = 1)`
= `(1)/(5(1)^4 + 6(1)^2 + 3)`
= `(1)/(5 + 6 + 3)`
= `(1)/(14)`.
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