What is the derivative of 4(ln(x+1)) ?

The derivative of 4(ln(x+1)) is 4/x

What is the first derivative of 4(ln(x+1)) ?

The first derivative of 4(ln(x+1)) is 4/x

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\frac{d}{d x} (4 (ln (x) + 1))

\frac{4}{x}

Solution steps

\frac{d}{d x} (4 (ln (x) + 1))

Take the constant out:

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

= 4 \frac{d}{d x} (ln (x) + 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 4 (\frac{d}{d x} (ln (x)) + \frac{d}{d x} (1))

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

\frac{d}{d x} (1) = 0

= 4 (\frac{1}{x} + 0)

Simplify

4 (\frac{1}{x} + 0) : \frac{4}{x}

= \frac{4}{x}

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What is the derivative of 4(ln(x+1)) ?
The derivative of 4(ln(x+1)) is 4/x
What is the first derivative of 4(ln(x+1)) ?
The first derivative of 4(ln(x+1)) is 4/x