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

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

edited Mar 26, 2013