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If y = x^x find dy/dx

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If y = xx find dy/dx

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Take logarithm on Both sides, we get 

logy = logxx ⇒ logy = xlogx 

Differentiate wr.t. x

1/y.dy/dx = xx 1/x + logx

dy/dx = y[1 + logx]

dy/dx = xx[1 + logx]

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