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Question Number 66046 by olalekan2 last updated on 08/Aug/19

$$find\frac{dy}{dx}ify=x^{x^x}$$$$helppls$$

Commented by Prithwish sen last updated on 08/Aug/19

$$\mathrm{y}={\mathrm{x}}^{{\mathrm{x}}^{\mathrm{x}}}\Rightarrow \mathrm{lny}={\mathrm{x}}^{\mathrm{x}}\mathrm{lnx}$$$$\mathrm{let}\mathrm{u}={\mathrm{x}}^{\mathrm{x}}\Rightarrow \mathrm{lnu}=\mathrm{xlnx}\Rightarrow \frac{\mathrm{du}}{\mathrm{dx}}=\mathrm{u}(\mathrm{lnx}+1)={\mathrm{x}}^{\mathrm{x}}(\mathrm{lnx}+1)$$$$\mathrm{lny}=\mathrm{ulnx}\Rightarrow \frac{1}{\mathrm{y}}\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{du}}{\mathrm{dx}}\mathrm{lnx}+\frac{\mathrm{u}}{\mathrm{x}}$$$$\frac{\mathrm{dy}}{\mathrm{dx}}={\mathrm{x}}^{{\mathrm{x}}^{\mathrm{x}}}[{\mathrm{x}}^{\mathrm{x}}(\mathrm{lnx}+1)\mathrm{lnx}+\frac{{\mathrm{x}}^{\mathrm{x}}}{\mathrm{x}}]$$$$\mathrm{please}\mathrm{check}.$$

Commented by olalekan2 last updated on 17/Oct/19

$$thanks........$$

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