What is the derivative of 3ln(6x+1) ?

The derivative of 3ln(6x+1) is (18)/(6x+1)

What is the first derivative of 3ln(6x+1) ?

The first derivative of 3ln(6x+1) is (18)/(6x+1)

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derivative of

3 ln (6 x + 1)

\frac{18}{6 x + 1}

Solution steps

\frac{d}{d x} (3 ln (6 x + 1))

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{6 x + 1} \frac{d}{d x} (6 x + 1)

= \frac{1}{6 x + 1} \frac{d}{d x} (6 x + 1)

\frac{d}{d x} (6 x + 1) = 6

= 3 \cdot \frac{1}{6 x + 1} \cdot 6

Simplify

3 \cdot \frac{1}{6 x + 1} \cdot 6 : \frac{18}{6 x + 1}

= \frac{18}{6 x + 1}

What is the derivative of 3ln(6x+1) ?
The derivative of 3ln(6x+1) is (18)/(6x+1)
What is the first derivative of 3ln(6x+1) ?
The first derivative of 3ln(6x+1) is (18)/(6x+1)