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

Question

10870 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-10T02:44:30

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#

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