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Find the derivative of y = x^x
Since the exponent is also a variable we can not use power rule instead we can take logarithm on both sides
y = x^x
Taking log on both sides
log y = log x^x
log y = x log x. ( log a^b = b log a )
Differentiating both sides wrt x
1/y dy/ dx = x •1/x + log x • 1. ( using product rule )
dy/dx = y ( 1 + log x )
dy/ dx = x^x ( 1+ log x ). ( by substituting back y = x^x )
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