What is (\partial)/(\partial x)((-x-9y)/(2y-7x)) ?

The answer to (\partial)/(\partial x)((-x-9y)/(2y-7x)) is -(65y)/((2y-7x)^2)

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(\partial)/(\partial x)((-x-9y)/(2y-7x))

\frac{\partial}{\partial x} (\frac{- x - 9 y}{2 y - 7 x})

- \frac{65 y}{( 2 y - 7 x ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{- x - 9 y}{2 y - 7 x})

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} ( - x - 9 y ) ( 2 y - 7 x ) - \frac{\partial}{\partial x} ( 2 y - 7 x ) ( - x - 9 y )}{( 2 y - 7 x ) ^{2}}

\frac{\partial}{\partial x} (- x - 9 y) = - 1

\frac{\partial}{\partial x} (2 y - 7 x) = - 7

= \frac{( - 1 ) ( 2 y - 7 x ) - ( - 7 ) ( - x - 9 y )}{( 2 y - 7 x ) ^{2}}

Simplify

\frac{( - 1 ) ( 2 y - 7 x ) - ( - 7 ) ( - x - 9 y )}{( 2 y - 7 x ) ^{2}} : - \frac{65 y}{( 2 y - 7 x ) ^{2}}

= - \frac{65 y}{( 2 y - 7 x ) ^{2}}

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What is (\partial)/(\partial x)((-x-9y)/(2y-7x)) ?
The answer to (\partial)/(\partial x)((-x-9y)/(2y-7x)) is -(65y)/((2y-7x)^2)