What is the derivative of 5ln(12x) ?

The derivative of 5ln(12x) is 5/x

What is the first derivative of 5ln(12x) ?

The first derivative of 5ln(12x) is 5/x

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\frac{d}{d x} (5 ln (12 x))

\frac{5}{x}

Solution steps

\frac{d}{d x} (5 ln (12 x))

Take the constant out:

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

= 5 \frac{d}{d x} (ln (12 x))

Apply the chain rule:

\frac{1}{12 x} \frac{d}{d x} (12 x)

= \frac{1}{12 x} \frac{d}{d x} (12 x)

\frac{d}{d x} (12 x) = 12

= 5 \cdot \frac{1}{12 x} \cdot 12

Simplify

5 \cdot \frac{1}{12 x} \cdot 12 : \frac{5}{x}

= \frac{5}{x}

What is the derivative of 5ln(12x) ?
The derivative of 5ln(12x) is 5/x
What is the first derivative of 5ln(12x) ?
The first derivative of 5ln(12x) is 5/x