What is the derivative of ln(6x^3) ?

The derivative of ln(6x^3) is 3/x

What is the first derivative of ln(6x^3) ?

The first derivative of ln(6x^3) is 3/x

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\frac{d}{d x} (ln (6 x^{3}))

\frac{3}{x}

Solution steps

\frac{d}{d x} (ln (6 x^{3}))

Apply the chain rule:

\frac{1}{6 x ^{3}} \frac{d}{d x} (6 x^{3})

= \frac{1}{6 x ^{3}} \frac{d}{d x} (6 x^{3})

\frac{d}{d x} (6 x^{3}) = 18 x^{2}

= \frac{1}{6 x ^{3}} \cdot 18 x^{2}

Simplify

\frac{1}{6 x ^{3}} \cdot 18 x^{2} : \frac{3}{x}

= \frac{3}{x}

\int \frac{( 5 t - 2 )}{t + 1} d t

\frac{d y}{d x} = \frac{( x ^{2} - 1 )}{y ^{2}}

\int \frac{e ^{x}}{3} - 4 x^{3} + \frac{6}{x} d x

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

n = 1 \sum \infty \frac{3}{n ^{2}}

What is the derivative of ln(6x^3) ?
The derivative of ln(6x^3) is 3/x
What is the first derivative of ln(6x^3) ?
The first derivative of ln(6x^3) is 3/x