What is the derivative of #(ln(x))^x#?

1 Answer
Guilherme N.
Dec 24, 2015

We can go by using chain rule and also the rule to derivate exponential functions.

Explanation:

Chain rule states that #(dy)/(dx)=(dy)/(du)(du)/(dx)#.
We'll also need the rule to derivate exponential functions, which is: be #f(x)=a^u#, then #f'(x)=a^u(lna)u'#

Let's rename #u=lnx#.

Solving:

#(dy)/(dx)=(lnx)^(x)(ln(lnx))*1#

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