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Solution to a CET test for diploma holders

B.sudhakar

11/01/2017 3 0

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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