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

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

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

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

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derivative of

f (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}}

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