logarithmic differentiation
The general formula for the derivative of \(f(x)^g(x)\), with \(f\) and \(g\) differentiable, is as follows:
\[
D[f(x)]^{g(x)} = f(x)^{g(x)} \left[ g'(x) \ln f(x) + g(x) \frac{f'(x)}{f(x)} \right ]
\]
The general formula for the derivative of \(f(x)^g(x)\), with \(f\) and \(g\) differentiable, is as follows:
\[
D[f(x)]^{g(x)} = f(x)^{g(x)} \left[ g'(x) \ln f(x) + g(x) \frac{f'(x)}{f(x)} \right ]
\]