What is the derivative of 2ln(2x^3) ?

The derivative of 2ln(2x^3) is 6/x

What is the first derivative of 2ln(2x^3) ?

The first derivative of 2ln(2x^3) is 6/x

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\frac{d}{d x} (2 ln (2 x^{3}))

\frac{6}{x}

Solution steps

\frac{d}{d x} (2 ln (2 x^{3}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

\frac{1}{2 x ^{3}} \frac{d}{d x} (2 x^{3})

= \frac{1}{2 x ^{3}} \frac{d}{d x} (2 x^{3})

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

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

Simplify

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

= \frac{6}{x}

What is the derivative of 2ln(2x^3) ?
The derivative of 2ln(2x^3) is 6/x
What is the first derivative of 2ln(2x^3) ?
The first derivative of 2ln(2x^3) is 6/x