Differentiate w.r.t. $x$ :
$y = x^{n} + n^{x} + x^{x} + n^{n}$

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Solution

$y = x^{n} + n^{x} + x^{x} + n^{n}$

Differentiating w.r.t. x, we get,

We know that
$\frac{d}{d x} (x^{n}) = n x^{n - 1}, \frac{d}{d x} (n^{x}) = n^{x} ln n, \frac{d}{d x} (x^{x}) = x^{x} (1 + log x)$

$∴$ $\frac{d y}{d x} = n x^{n - 1} + n^{x} l n n + x^{x} (1 + log x)$

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