What is (\partial)/(\partial y)((2x+3y)/(y-x)) ?

The answer to (\partial)/(\partial y)((2x+3y)/(y-x)) is -(5x)/((y-x)^2)

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(\partial)/(\partial y)((2x+3y)/(y-x))

\frac{\partial}{\partial y} (\frac{2 x + 3 y}{y - x})

- \frac{5 x}{( y - x ) ^{2}}

Solution steps

\frac{\partial}{\partial y} (\frac{2 x + 3 y}{y - 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} ( 2 x + 3 y ) ( y - x ) - \frac{\partial}{\partial y} ( y - x ) ( 2 x + 3 y )}{( y - x ) ^{2}}

\frac{\partial}{\partial y} (2 x + 3 y) = 3

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

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

Simplify

\frac{3 ( y - x ) - 1 \cdot ( 2 x + 3 y )}{( y - x ) ^{2}} : - \frac{5 x}{( y - x ) ^{2}}

= - \frac{5 x}{( y - x ) ^{2}}

\int \frac{e ^{- b x}}{1 - e ^{- 2 b x}} d x

\int x ln (6 x) d x

\frac{2}{x ^{2}}

\frac{d}{d x} (ln ((x^{2})^{2}))

(- π, 0), (- \frac{π}{2}, 4)

What is (\partial)/(\partial y)((2x+3y)/(y-x)) ?
The answer to (\partial)/(\partial y)((2x+3y)/(y-x)) is -(5x)/((y-x)^2)