What is (\partial)/(\partial x)((-9x-7y)/((5x+3y))) ?

The answer to (\partial)/(\partial x)((-9x-7y)/((5x+3y))) is (8y)/((5x+3y)^2)

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(\partial)/(\partial x)((-9x-7y)/((5x+3y)))

\frac{\partial}{\partial x} (\frac{- 9 x - 7 y}{( 5 x + 3 y )})

\frac{8 y}{( 5 x + 3 y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{- 9 x - 7 y}{( 5 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} ( - 9 x - 7 y ) ( 5 x + 3 y ) - \frac{\partial}{\partial x} ( 5 x + 3 y ) ( - 9 x - 7 y )}{( 5 x + 3 y ) ^{2}}

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

\frac{\partial}{\partial x} (5 x + 3 y) = 5

= \frac{( - 9 ) ( 5 x + 3 y ) - 5 ( - 9 x - 7 y )}{( 5 x + 3 y ) ^{2}}

Simplify

\frac{( - 9 ) ( 5 x + 3 y ) - 5 ( - 9 x - 7 y )}{( 5 x + 3 y ) ^{2}} : \frac{8 y}{( 5 x + 3 y ) ^{2}}

= \frac{8 y}{( 5 x + 3 y ) ^{2}}

\int \frac{1}{9 x ^{2} - 16} d x

\frac{\partial}{\partial y} (z arctan (\frac{y}{x}))

\frac{d}{d x} (e^{1 - 3 x})

\int_{1}^{2} \frac{e ^{x}}{x} d x

(7.2) (2.12)

What is (\partial)/(\partial x)((-9x-7y)/((5x+3y))) ?
The answer to (\partial)/(\partial x)((-9x-7y)/((5x+3y))) is (8y)/((5x+3y)^2)