Question

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

Answer 1

y = x log x
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"(xlogx)`

= `x"d"/"dx"(logx) + (logx)."d"/"dx"(x)`

= `x xx 1/x + (logx) xx 1`

= 1 + logx
The derivative of inverse function of y = f(x) is given by
`"dx"/"dy" = (1)/(("dy"/"dx")`
= `(1)/(1 + logx)`.