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

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

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

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

\frac{2}{x}

Solution steps

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

Apply the chain rule:

\frac{1}{2 x ^{2}} \frac{\partial}{\partial x} (2 x^{2})

= \frac{1}{2 x ^{2}} \frac{\partial}{\partial x} (2 x^{2})

\frac{\partial}{\partial x} (2 x^{2}) = 4 x

= \frac{1}{2 x ^{2}} \cdot 4 x

Simplify

\frac{1}{2 x ^{2}} \cdot 4 x : \frac{2}{x}

= \frac{2}{x}

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