How do you differentiate y=x^(1/lnx)?

1 Answer
Jul 10, 2016

For this problem, we can use logarithmic differentiation.

y = x^(1/ln(x))

Taking the natural logarithm of both sides gives

ln(y) = ln(x^(1/ln(x)))

ln(y) = 1/ln(x) * ln(x)

ln(y) = 1

Now, taking the derivative of both sides yields

(y')/(y) = 0

Thus

y' = 0

Explanation:

I highly suggest reviewing more examples if you need more practice.