What is (\partial)/(\partial x)(ln(x^3)) ?

The answer to (\partial)/(\partial x)(ln(x^3)) is 3/x

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(\partial)/(\partial x)(ln(x^3))

\frac{\partial}{\partial x} (ln (x^{3}))

\frac{3}{x}

Solution steps

\frac{\partial}{\partial x} (ln (x^{3}))

Apply the chain rule:

\frac{1}{x ^{3}} \frac{\partial}{\partial x} (x^{3})

= \frac{1}{x ^{3}} \frac{\partial}{\partial x} (x^{3})

\frac{\partial}{\partial x} (x^{3}) = 3 x^{2}

= \frac{1}{x ^{3}} \cdot 3 x^{2}

Simplify

\frac{1}{x ^{3}} \cdot 3 x^{2} : \frac{3}{x}

= \frac{3}{x}

\int \frac{1}{( 1 - y )} d y

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\frac{\partial}{\partial z} (5 sin^{2} (z))

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What is (\partial)/(\partial x)(ln(x^3)) ?
The answer to (\partial)/(\partial x)(ln(x^3)) is 3/x