**Logarithmic differentiation**
Having some problems with these question....

f(x) and

*g(x) *are two differentiable functions and

* f(x)*>0 for all x.

Consider

*h(x)* =

*f(x)^g(x)*
a) Show that ln

*h(x) = g(x) *ln

* f(x)*

b) Show that the derivate of ln

*h(x) *with respect to

*x* is:

*g´(x) *ln

* f(x)* +

*g(x) f´(x)/f(x)*

c) Show that the derivate of ln

* h(x)* with respect to

*x* is:

*h´(x)/h(x)*

d) Show that

*h´(x) = f(x)^g(x) *[

*g´(x) *ln

* f(x)* +

*g(x) f´(x)/f(x)*]

e) Use the above formula to find the derivate of

*h(x)=x^x.*

Identify the functions

*f(x)* and

*g(x) *and their derivatives.

Thanks for help!! This is killing me...