Question Number 226820 by Spillover last updated on 16/Dec/25
$$ \\ $$$$\:\:\:\:\:{Differentiate}\:\:\:\:{x}^{{x}^{{x}} } \\ $$$$ \\ $$
Answered by AgniMath last updated on 16/Dec/25
$${y}={x}^{{x}^{{x}} } \\ $$$$\Rightarrow{lny}={x}^{{x}} {lnx} \\ $$$$\Rightarrow\frac{\mathrm{1}}{{y}}\frac{{dy}}{{dx}}={x}^{{x}} .\frac{\mathrm{1}}{{x}}+{x}^{{x}} \left(\mathrm{1}+{lnx}\right){lnx} \\ $$$$\Rightarrow\frac{{dy}}{{dx}}={x}^{{x}^{{x}} } \left({x}^{{x}} \left(\frac{\mathrm{1}}{{x}}+{lnx}+\left({lnx}\right)^{\mathrm{2}} \right)\right) \\ $$
Commented by Spillover last updated on 16/Dec/25
$${thanks} \\ $$