For a constant $a$, $\frac{d}{dx} \left( x^x + x^a + a^x + a^a \right)$ is
$x^x (1 + \log x) + ax^{a-1}$
$x^x (1 + \log x) + ax^{a-1} + a^x \log a$
$x^x (1 + \log x) + a^a (1 + \log x)$
$x^x (1 + \log x) + a^a (1 + \log a) + ax^{a-1}$
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