What is (\partial)/(\partial x)(((3x-4y))/(-x+6y)) ?

The answer to (\partial)/(\partial x)(((3x-4y))/(-x+6y)) is (14y)/((-x+6y)^2)

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(\partial)/(\partial x)(((3x-4y))/(-x+6y))

\frac{\partial}{\partial x} (\frac{( 3 x - 4 y )}{- x + 6 y})

\frac{14 y}{( - x + 6 y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{( 3 x - 4 y )}{- x + 6 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} ( 3 x - 4 y ) ( - x + 6 y ) - \frac{\partial}{\partial x} ( - x + 6 y ) ( 3 x - 4 y )}{( - x + 6 y ) ^{2}}

\frac{\partial}{\partial x} (3 x - 4 y) = 3

\frac{\partial}{\partial x} (- x + 6 y) = - 1

= \frac{3 ( - x + 6 y ) - ( - 1 ) ( 3 x - 4 y )}{( - x + 6 y ) ^{2}}

Simplify

\frac{3 ( - x + 6 y ) - ( - 1 ) ( 3 x - 4 y )}{( - x + 6 y ) ^{2}} : \frac{14 y}{( - x + 6 y ) ^{2}}

= \frac{14 y}{( - x + 6 y ) ^{2}}

- \frac{x}{9 y}

(8, 1), (0, - 3)

x \to - \infty lim (\frac{1}{- x})

\frac{d}{d θ} (θ + cos (θ))

x \to 2 lim (\frac{x}{x ^{2} - 2 x})

What is (\partial)/(\partial x)(((3x-4y))/(-x+6y)) ?
The answer to (\partial)/(\partial x)(((3x-4y))/(-x+6y)) is (14y)/((-x+6y)^2)