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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

= y \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

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

Simplify

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

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

\int - cos (d) x d x

n = 0 \sum \infty \frac{1}{2 n + 4}

\int 28 x^{3} - 15 x^{2} + 10 x d x

\frac{5}{2 ( s - e ) ^{2} + 50}

\frac{25}{s ^{3} ( s ^{2} + 4 s + 5 )}

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