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

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

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

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

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

\frac{3}{x + 1}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{3}{x + 1}

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