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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 = 3x2 + 2logx3
Solution
y = 3x2 + 2logx3
= 3x2 + 6logx
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"(3x^2 + 6logx)`
= `3 xx 2x + 6 xx 1/x`
= `6x + 6/x`
= `(6x^2 + 6)/x`
The derivative of inverse function of y = f(x) is given by
`"dx"/"dy" = (1)/(("dy"/"dx")`
= `(1)/(((6x^2 + 6)/x)`
= `x/(6x^2 + 6)`
At x = `1, "dx"/"dy"`
= `(x/(6x^2 + 6))_(at x = 1)`
= `(1)/(6(1)^2 + 6)`
= `(1)/(12)`.
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