use-logarithmic-differentiation-to-evaluate-the-derivative-of-the-function-gxxex

Question

Use logarithmic differentiation to evaluate the derivative of the function $g (x) = x^{e^{x}}$ .

Accepted Answer

$g^{'} (x) = x^{e^{x} - 1} e^{x} (x \ln x + 1)$

Answer

$g^{\prime}\left(x\right)=e^{x}x^{e^{x}-1}$

Answer

$g^{'} (x) = x^{e^{x} - 1} e^{x} (x \ln x + 1)$

Answer

$g^{'} (x) = x^{e^{x} - 1} e^{x} (x \ln x + 1)$

Use logarithmic differentiation to evaluate the derivative of the function g(x)=xexg\left(x\right)=x^{e^{x}}.