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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derivative of

\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}}

\frac{s}{2 s ^{2} + 1}

\frac{d}{d x} (\frac{1}{3} sec^{3} (2 x) - sec (2 x))

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

x \to 1 lim (\frac{x ^{3}}{x ^{2} - 1})

f (x) = 6^{7 x^{2}}

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)