What is (\partial)/(\partial x)(x^{2x}) ?

The answer to (\partial)/(\partial x)(x^{2x}) is 2x^{2x}(ln(x)+1)

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(\partial)/(\partial x)(x^{2x})

\frac{\partial}{\partial x} (x^{2 x})

2 x^{2 x} (ln (x) + 1)

Solution steps

\frac{\partial}{\partial x} (x^{2 x})

Apply exponent rule:

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

x^{2 x} = e^{2 x l n (x)}

= \frac{\partial}{\partial x} (e^{2 x l n (x)})

Apply the chain rule:

e^{2 x l n (x)} \frac{\partial}{\partial x} (2 x ln (x))

= e^{2 x l n (x)} \frac{\partial}{\partial x} (2 x ln (x))

\frac{\partial}{\partial x} (2 x ln (x)) = 2 (ln (x) + 1)

= e^{2 x l n (x)} \cdot 2 (ln (x) + 1)

e^{2 x l n (x)} = x^{2 x}

= 2 x^{2 x} (ln (x) + 1)

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What is (\partial)/(\partial x)(x^{2x}) ?
The answer to (\partial)/(\partial x)(x^{2x}) is 2x^{2x}(ln(x)+1)