Emril,

I can get you started on this. Suppose g(x) = f(x)^x then you can find g'(x) as follows.

Tale the natural log of both sides of g(x) = f(x)^x

ln(g(x) = ln(f(x)^x)

Using the logarithm laws

ln(g(x) = x ln(f(x))

Now differentiate both sides.

g'(x)/g(x) = ln(f(x)) + x f '(x)/f(x)

or

g'(x) = g(x) [ln(f(x)) + x f '(x)/f(x)] = f(x)^x [ln(f(x)) + x f '(x)/f(x)]

Harley