what is the derivative of x^(e^x)? Is it [e^x][x^(e^x - 1)]? Or is there something else that I have to do. thanks!
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Originally Posted by mneox what is the derivative of x^(e^x)? Is it [e^x][x^(e^x - 1)]? Or is there something else that I have to do. thanks! Follow this link and click on "Show steps": differentiate x^(e^x) - Wolfram|Alpha
Originally Posted by mneox what is the derivative of x^(e^x)? Is it [e^x][x^(e^x - 1)]? Or is there something else that I have to do. thanks! Write $\displaystyle f(x):=x^{e^x}=e^{e^x\ln x}\Longrightarrow f'(x)=e^{e^x\ln x}\left[e^x\ln x+\frac{e^x}{x}\right]$ $\displaystyle =x^{e^x}\left[e^x\ln x+\frac{e^x}{x}\right]$ $\displaystyle =x^{e^x}\ln\left(x^{e^x}\right)+e^xx^{e^x-1}$ . Tonio
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