Differentiate the function w.r.t.x. : 
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a is a constant term so, a^a is also a constant term. hence, differentiation of a^a = 0
![y=x^x+a^x+x^a+a^a\\\\y=e^{xlogx}+e^{xloga}+x^a+a^a\\\\\textbf{differentiate both sides wrt to x}\\\\\frac{dy}{dx}=\frac{d\{e^{xlogx}\}}{dx}+\frac{d\{e^{xloga}\}}{dx}+\frac{d\{x^a\}}{dx}+\frac{d\{a^a\}}{dx}\\\\\frac{dy}{dx}=e^{xlogx}\left[x\frac{d(logx)}{dx}+logx\frac{dx}{dx}\right]+e^{xloga}\left[x\frac{d(loga)}{dx}+loga\frac{dx}{dx}\right]+ax^{(a-1)}+0\\\\\frac{dy}{dx}=x^x(1+logx)+a^x(loga)+ax^{(a-1)}](https://tex.z-dn.net/?f=y%3Dx%5Ex%2Ba%5Ex%2Bx%5Ea%2Ba%5Ea%5C%5C%5C%5Cy%3De%5E%7Bxlogx%7D%2Be%5E%7Bxloga%7D%2Bx%5Ea%2Ba%5Ea%5C%5C%5C%5C%5Ctextbf%7Bdifferentiate+both+sides+wrt+to+x%7D%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7Bd%5C%7Be%5E%7Bxlogx%7D%5C%7D%7D%7Bdx%7D%2B%5Cfrac%7Bd%5C%7Be%5E%7Bxloga%7D%5C%7D%7D%7Bdx%7D%2B%5Cfrac%7Bd%5C%7Bx%5Ea%5C%7D%7D%7Bdx%7D%2B%5Cfrac%7Bd%5C%7Ba%5Ea%5C%7D%7D%7Bdx%7D%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%3De%5E%7Bxlogx%7D%5Cleft%5Bx%5Cfrac%7Bd%28logx%29%7D%7Bdx%7D%2Blogx%5Cfrac%7Bdx%7D%7Bdx%7D%5Cright%5D%2Be%5E%7Bxloga%7D%5Cleft%5Bx%5Cfrac%7Bd%28loga%29%7D%7Bdx%7D%2Bloga%5Cfrac%7Bdx%7D%7Bdx%7D%5Cright%5D%2Bax%5E%7B%28a-1%29%7D%2B0%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%3Dx%5Ex%281%2Blogx%29%2Ba%5Ex%28loga%29%2Bax%5E%7B%28a-1%29%7D "y=x^x+a^x+x^a+a^a\\\\y=e^{xlogx}+e^{xloga}+x^a+a^a\\\\\textbf{differentiate both sides wrt to x}\\\\\frac{dy}{dx}=\frac{d\{e^{xlogx}\}}{dx}+\frac{d\{e^{xloga}\}}{dx}+\frac{d\{x^a\}}{dx}+\frac{d\{a^a\}}{dx}\\\\\frac{dy}{dx}=e^{xlogx}\left[x\frac{d(logx)}{dx}+logx\frac{dx}{dx}\right]+e^{xloga}\left[x\frac{d(loga)}{dx}+loga\frac{dx}{dx}\right]+ax^{(a-1)}+0\\\\\frac{dy}{dx}=x^x(1+logx)+a^x(loga)+ax^{(a-1)}")
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