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If y=x^x then find dy/dx​

Answer»

y = {x}^{x} \\ \\ taking \: logarithm \: both \: sides \\ \\ logy = xlogx \\ \\ diff. \: \: both \: sides \: w.r.t \: \: \: x \\ \\ \frac{1}{y} \frac{dy}{dx} = x \frac{1}{x} + logx \\ \\ \frac{dy}{dx} = y(1 + logx) \\ \\ \frac{dy}{dx} = {x}^{x} (1 + logx)


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