What is the derivative of-3ln(x) ?

The derivative of-3ln(x) is -3/x

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

The first derivative of-3ln(x) is -3/x

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\frac{d}{d x} (- 3 ln (x))

- \frac{3}{x}

Solution steps

\frac{d}{d x} (- 3 ln (x))

Take the constant out:

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

= - 3 \frac{d}{d x} (ln (x))

Apply the common derivative:

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= - 3 \cdot \frac{1}{x}

Simplify

- 3 \cdot \frac{1}{x} : - \frac{3}{x}

= - \frac{3}{x}

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(- 8, - 3), (- 12, - 3)