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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

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

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

\frac{d}{d x} (π csc (π + \frac{x ^{6}}{3}))

f (x) = (x - 1)

y^{^{''}} + 4 y^{^{'}} + 4 y = \frac{( e ^{- 2 x} )}{( x ^{2} )}

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