What is (\partial)/(\partial y)(y/(y-2x)) ?

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

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(\partial)/(\partial y)(y/(y-2x))

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

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

Solution steps

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

Treat

x

as a constant

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d v}{d t} = 9.8 - \frac{v}{5}, v (0) = 0

- 2 7 s^{2} + 8

x y^{^{'}} = x + y

\frac{d}{d x} (\frac{K x + 11}{x ^{2} + ( K + 1 ) x + 11})

\int sin (9 x) cos (5 x) d x

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