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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

\int \frac{x ^{2} + 3 x + 2}{x ^{2} ( x + 3 )} d x

\int \frac{a ^{t}}{t} d t

\int 6 sin^{3} (x) cos^{5} (x) d x

(x^{x})^{^{'}}

x \to 2 - lim (ln (4 - 2 x))

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