What is (\partial)/(\partial x)(x^x) ?

The answer to (\partial)/(\partial x)(x^x) is x^x(ln(x)+1)

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(\partial)/(\partial x)(x^x)

\frac{\partial}{\partial x} (x^{x})

x^{x} (ln (x) + 1)

Solution steps

\frac{\partial}{\partial x} (x^{x})

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{x} = e^{x l n (x)}

= \frac{\partial}{\partial x} (e^{x l n (x)})

Apply the chain rule:

e^{x l n (x)} \frac{\partial}{\partial x} (x ln (x))

= e^{x l n (x)} \frac{\partial}{\partial x} (x ln (x))

\frac{\partial}{\partial x} (x ln (x)) = ln (x) + 1

= e^{x l n (x)} (ln (x) + 1)

e^{x l n (x)} = x^{x}

= x^{x} (ln (x) + 1)

x \to \infty lim (9.35 e^{(- 0.4 x)} + 5.52)

x \to - 2 lim (\frac{x ^{2} + 2}{x + 2})

\frac{1}{x} lo g_{10} (1 + x)

\int \frac{7 x - 1}{x ^{2} - x - 6} d x

\int_{0}^{2} x (1 - 0.5 x) d x

What is (\partial)/(\partial x)(x^x) ?
The answer to (\partial)/(\partial x)(x^x) is x^x(ln(x)+1)