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Question
Find the derivative of the inverse function of the following : y = x2 + log x
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Solution
y = x2 + log x
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"(x^2 + logx)`
= `"d"/"dx"(x^2) + "d"/"dx"(logx)`
= `2x + 1/x`
= `(2x^2 + 1)/(x`
The derivative of inverse function of y = f(x) is given by
`"dx"/"dy" = (1)/(("dy"/"dx")`
= `(1)/(((2x^2 + 1)/x)`
= `x/(2x^2 + 1)`.
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