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

Question

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

Accepted Answer

g′(x)=xex−1ex(xln⁡$$x+1)g^{\prime}$$\left(x\right)=$$x^{e^{x}-1$$}$$e^{x}$$\left(x\ln x+1\right)

Answer

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

Answer

g′(x)=xex−1ex(xln⁡x−$$1)g^{\prime}$$\left(x\right)=$$x^{e^{x}-1$$}$$e^{x}$$\left(x\ln x-1\right)

Answer

g′(x)=xexln⁡(ex−$$1)g^{\prime}$$\left(x\right)=$$x^{e^{x}$$}\ln\$$left(e^{x}-1$$\right)

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