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...