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

The derivative of f(x)=6(ln(x+1)) is 6/(x+1)

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

The first derivative of f(x)=6(ln(x+1)) is 6/(x+1)

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derivative of

f (x) = 6 (ln (x + 1))

\frac{6}{x + 1}

Solution steps

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

Take the constant out:

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

= 6 \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

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

Simplify

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

= \frac{6}{x + 1}

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\frac{\partial}{\partial x} (\frac{1}{t} e^{\frac{x ^{2}}{4 t}})

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