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Find $\Large \frac{dy}{dx}$ when $ y=a^x.x^a$

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  • If there is a variable in index then use log before differentiating.
  • $ log\: a\: b = log\: a+log\: b$
  • $ log\: a^n = n\: log\: a$
$ y = a^x\: x^a$
$ log\: y = x\: x\: log\: a + \large\frac{a}{x}$
$ \large\frac{dy}{dx}=a^xx^a\: \bigg[ log\: a + \large\frac{a}{x} \bigg]$


answered Mar 12, 2013 by thanvigandhi_1
edited Mar 26, 2013 by thanvigandhi_1
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