What is (\partial)/(\partial x)((x-y)/(x+y)) ?

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

Popular >

(\partial)/(\partial x)((x-y)/(x+y))

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

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

Solution steps

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

Treat

y

as a constant

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

y = \frac{4}{3} π r^{2}

\frac{d y}{d x}, x^{3} + e^{(5 x y)} - 4 y^{3} = 10

\int \frac{6}{x ^{7}} d x

\int cot (3 - 7 x) d x

f (x) = \frac{( x ^{2} - 1 )}{2 x - 3}

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