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

The derivative of (ln(x)/(x+1)) is (x+1-xln(x))/(x(x+1)^2)

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

The first derivative of (ln(x)/(x+1)) is (x+1-xln(x))/(x(x+1)^2)

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

\frac{x + 1 - x ln ( x )}{x ( x + 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( ln ( x ) ) ( x + 1 ) - \frac{d}{d x} ( x + 1 ) ln ( x )}{( x + 1 ) ^{2}}

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

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

= \frac{\frac{1}{x} ( x + 1 ) - 1 \cdot ln ( x )}{( x + 1 ) ^{2}}

Simplify

\frac{\frac{1}{x} ( x + 1 ) - 1 \cdot ln ( x )}{( x + 1 ) ^{2}} : \frac{x + 1 - x ln ( x )}{x ( x + 1 ) ^{2}}

= \frac{x + 1 - x ln ( x )}{x ( x + 1 ) ^{2}}

What is the derivative of (ln(x)/(x+1)) ?
The derivative of (ln(x)/(x+1)) is (x+1-xln(x))/(x(x+1)^2)
What is the first derivative of (ln(x)/(x+1)) ?
The first derivative of (ln(x)/(x+1)) is (x+1-xln(x))/(x(x+1)^2)