What is the derivative of ln(5x^3) ?

The derivative of ln(5x^3) is 3/x

What is the first derivative of ln(5x^3) ?

The first derivative of ln(5x^3) is 3/x

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\frac{d}{d x} (ln (5 x^{3}))

\frac{3}{x}

Solution steps

\frac{d}{d x} (ln (5 x^{3}))

Apply the chain rule:

\frac{1}{5 x ^{3}} \frac{d}{d x} (5 x^{3})

= \frac{1}{5 x ^{3}} \frac{d}{d x} (5 x^{3})

\frac{d}{d x} (5 x^{3}) = 15 x^{2}

= \frac{1}{5 x ^{3}} \cdot 15 x^{2}

Simplify

\frac{1}{5 x ^{3}} \cdot 15 x^{2} : \frac{3}{x}

= \frac{3}{x}

What is the derivative of ln(5x^3) ?
The derivative of ln(5x^3) is 3/x
What is the first derivative of ln(5x^3) ?
The first derivative of ln(5x^3) is 3/x