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

The answer to (\partial)/(\partial x)((2x-y)/(x+3y)) is (7y)/((x+3y)^2)

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

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

\frac{7 y}{( x + 3 y ) ^{2}}

Solution steps

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

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

\frac{\partial}{\partial x} (x + 3 y) = 1

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

Simplify

\frac{2 ( x + 3 y ) - 1 \cdot ( 2 x - y )}{( x + 3 y ) ^{2}} : \frac{7 y}{( x + 3 y ) ^{2}}

= \frac{7 y}{( x + 3 y ) ^{2}}

x \to 2 - lim (x + c)

\int x - \frac{2}{x} d x

\int sec^{2} (θ) tan (θ) d θ

\int e^{- (x^{3})^{3}} d (x^{3})^{3}

x \to a + lim (- 5)

What is (\partial)/(\partial x)((2x-y)/(x+3y)) ?
The answer to (\partial)/(\partial x)((2x-y)/(x+3y)) is (7y)/((x+3y)^2)