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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

n = 1 \sum \infty (\frac{7}{3})^{n}

\int_{6}^{8} \frac{66}{( x - 6 ) ^{3}} d x

x \to 4 lim (x^{\frac{1}{5}})

f (x) = ln (11 x)

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

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