What is the derivative of 3ln(7x) ?

The derivative of 3ln(7x) is 3/x

What is the first derivative of 3ln(7x) ?

The first derivative of 3ln(7x) is 3/x

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\frac{d}{d x} (3 ln (7 x))

\frac{3}{x}

Solution steps

\frac{d}{d x} (3 ln (7 x))

Take the constant out:

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

= 3 \frac{d}{d x} (ln (7 x))

Apply the chain rule:

\frac{1}{7 x} \frac{d}{d x} (7 x)

= \frac{1}{7 x} \frac{d}{d x} (7 x)

\frac{d}{d x} (7 x) = 7

= 3 \cdot \frac{1}{7 x} \cdot 7

Simplify

3 \cdot \frac{1}{7 x} \cdot 7 : \frac{3}{x}

= \frac{3}{x}

What is the derivative of 3ln(7x) ?
The derivative of 3ln(7x) is 3/x
What is the first derivative of 3ln(7x) ?
The first derivative of 3ln(7x) is 3/x