Final answer to the problem
Step-by-step Solution
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Apply the formula: $\frac{d}{dx}\left(a^b\right)$$=y=a^b$, where $d/dx=\frac{d}{dx}$, $a=x$, $b=x$, $a^b=x^x$ and $d/dx?a^b=\frac{d}{dx}\left(x^x\right)$
Apply the formula: $y=a^b$$\to \ln\left(y\right)=\ln\left(a^b\right)$, where $a=x$ and $b=x$
Apply the formula: $\ln\left(x^a\right)$$=a\ln\left(x\right)$, where $a=x$
Apply the formula: $\ln\left(y\right)=x$$\to \frac{d}{dx}\left(\ln\left(y\right)\right)=\frac{d}{dx}\left(x\right)$, where $x=x\ln\left(x\right)$
Apply the formula: $\frac{d}{dx}\left(ab\right)$$=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right)$, where $d/dx=\frac{d}{dx}$, $ab=x\ln\left(x\right)$, $a=x$, $b=\ln\left(x\right)$ and $d/dx?ab=\frac{d}{dx}\left(x\ln\left(x\right)\right)$
Apply the formula: $\frac{d}{dx}\left(x\right)$$=1$
Apply the formula: $\frac{d}{dx}\left(\ln\left(x\right)\right)$$=\frac{1}{x}\frac{d}{dx}\left(x\right)$
Apply the formula: $\frac{d}{dx}\left(x\right)$$=1$
Apply the formula: $a\frac{b}{x}$$=\frac{ab}{x}$, where $a=x$ and $b=1$
Apply the formula: $\frac{a}{b}=c$$\to a=cb$, where $a=y^{\prime}$, $b=y$ and $c=\ln\left(x\right)+1$
Substitute $y$ for the original function: $x^x$
The derivative of the function results in
