What is (\partial)/(\partial x)(x/(1+x)) ?

The answer to (\partial)/(\partial x)(x/(1+x)) is 1/((1+x)^2)

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(\partial)/(\partial x)(x/(1+x))

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

Simplify

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

3 (x)^{2} + 8 (x) + 12

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

y^{^{''}} + 4 y^{^{'}} - 2 y = 2 x^{2} - 3 x + 6

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

x \to 2 lim (3 x + 2)

What is (\partial)/(\partial x)(x/(1+x)) ?
The answer to (\partial)/(\partial x)(x/(1+x)) is 1/((1+x)^2)