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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

y^{^{'}} - 12 x^{11} y = e^{x^{12}}

\frac{d}{d x} (- 18 e^{- 2 x})

x \to 1 lim (\frac{x ^{5} - 1}{x - 1})

\frac{d}{d x} (sin (\frac{π x}{4}))

\frac{1}{x}, 1

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