Question

Find the derivative of the inverse function of the following : y = x² + log x

Answer 1

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)`.