Use logarithmic differentiation to find the derivative of the function y = x^x

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Use logarithmic differentiation to find the derivative of the function y = x^x

Mathematics
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(1+logx)x^x
y = x^x ln both sides... lny = lnx^x via reverse power rule... lny = xlnx you can use implicit differentiation now...you do know that right/
so d/dx(lny) = 1/y * y' and d/dx(xlnx) = x*1/x .....????

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it goes lyk tis logy= xlogx diff wrt to x on bth sides so on lhs its 1/y dy/dx=1+logx by product rule on rhs u get 1+logx thn dy/dx =(1+logx)y wer y is nthin bt =x^x
one of my favourite derivatives. an alternative to the ones suggested above: y = e^log(x^x) = e^xlog(x) which you can differentiate using the chain rule
thx guys you just walked me through my first ever log diff problem

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