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

The answer to (\partial)/(\partial x)(((x-5y))/(5xy+7)) is (25y^2+7)/((5xy+7)^2)

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(\partial)/(\partial x)(((x-5y))/(5xy+7))

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

\frac{25 y ^{2} + 7}{( 5 x y + 7 ) ^{2}}

Solution steps

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

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

\frac{\partial}{\partial x} (x - 5 y) = 1

\frac{\partial}{\partial x} (5 x y + 7) = 5 y

= \frac{1 \cdot ( 5 x y + 7 ) - 5 y ( x - 5 y )}{( 5 x y + 7 ) ^{2}}

Simplify

\frac{1 \cdot ( 5 x y + 7 ) - 5 y ( x - 5 y )}{( 5 x y + 7 ) ^{2}} : \frac{25 y ^{2} + 7}{( 5 x y + 7 ) ^{2}}

= \frac{25 y ^{2} + 7}{( 5 x y + 7 ) ^{2}}

\frac{( 2 - \frac{1}{x} )}{x - 3}

\int \frac{27}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (cot (sin (x)))

\frac{d y}{d x} = e^{- k \cdot a \cdot x}, y (0) = 0

x^{3} - 3 x - 4

What is (\partial)/(\partial x)(((x-5y))/(5xy+7)) ?
The answer to (\partial)/(\partial x)(((x-5y))/(5xy+7)) is (25y^2+7)/((5xy+7)^2)