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

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

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

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

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derivative of

f (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}}

x \to 0 lim (e^{x} cos (2 x))

\int (\frac{3 x ( e ^{- 2 x} - 7 x )}{5}) d x

x \to \infty lim ((\frac{1}{x})^{\frac{1}{x} + 1})

\int_{2}^{e^{3}} \frac{1}{x} d x

y = \frac{2 cos ( x )}{x + 1}

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