What is the derivative of x/((x+y)^2) ?

The derivative of x/((x+y)^2) is (-x+y)/((x+y)^3)

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

The first derivative of x/((x+y)^2) is (-x+y)/((x+y)^3)

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derivative of

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

\frac{- x + y}{( x + y ) ^{3}}

Solution steps

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

Treat

y

as a constant

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot ( x + y ) ^{2} - 2 ( x + y ) x}{( ( x + y ) ^{2} ) ^{2}} : \frac{- x + y}{( x + y ) ^{3}}

= \frac{- x + y}{( x + y ) ^{3}}

What is the derivative of x/((x+y)^2) ?
The derivative of x/((x+y)^2) is (-x+y)/((x+y)^3)
What is the first derivative of x/((x+y)^2) ?
The first derivative of x/((x+y)^2) is (-x+y)/((x+y)^3)