What is (\partial)/(\partial x)((ln(x^2))^2) ?

The answer to (\partial)/(\partial x)((ln(x^2))^2) is (8ln(x))/x

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(\partial)/(\partial x)((ln(x^2))^2)

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

\frac{8 ln ( x )}{x}

Solution steps

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

Apply the chain rule:

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

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

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

= 2 ln (x^{2}) \frac{2}{x}

Simplify

2 ln (x^{2}) \frac{2}{x} : \frac{8 ln ( x )}{x}

= \frac{8 ln ( x )}{x}

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What is (\partial)/(\partial x)((ln(x^2))^2) ?
The answer to (\partial)/(\partial x)((ln(x^2))^2) is (8ln(x))/x