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Derivative from First Principle

If y = xx +...

Question

If $y = x^{x} + x^{a} + a^{a} + a^{a}$ , then find $\frac{d y}{d x}$ .

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Solution

$y = x^{x} + x^{a} + a^{a} + a^{a}$
$\frac{d y}{d x} = (ln x + 1) x^{x} + a x^{(a - 1)} + 0 + 0$
Answer : $\frac{d y}{d x} = (ln x + 1) x^{x} + a x^{(a - 1)}$

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