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Question Number 121720 by Jamshidbek2311 last updated on 11/Nov/20

$$Doesthisexampleworkthatway.$$$$f\left(x\right)=x^x{f}^{\prime }\left(x\right)=x^x\cdot (lnx+1)$$

Answered by Dwaipayan Shikari last updated on 11/Nov/20

$$f\left(x\right)=x^x$$$$log\left(f\left(x\right)\right)=xlogx$$$$\frac{f^{\prime }\left(x\right)}{f\left(x\right)}=1+logx$$$$f^{\prime }\left(x\right)=f\left(x\right)(1+logx)=x^x(1+logx)$$

Answered by ebi last updated on 11/Nov/20

$$$$$$Yes.$$$$f\left(x\right)=x^x$$$$lety=x^x$$$$lny=ln{x}^x$$$$lny=xlnx$$$$\frac{d}{dx}\left(lny\right)=\frac{d}{dx}\left(xlnx\right)$$$$\frac{1}{y}\cdot \frac{dy}{dx}=x\cdot \frac{1}{x}+lnx$$$$\frac{1}{y}\cdot \frac{dy}{dx}=1+lnx$$$$\frac{dy}{dx}=y(1+lnx)$$$$\therefore f^{\prime }\left(x\right)=x^x(1+lnx)$$

Commented by Jamshidbek2311 last updated on 11/Nov/20

$$thank$$

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