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

The answer to (\partial)/(\partial x)((7y-7x)/(y^2+2x^2)) is (14x^2-28yx-7y^2)/((y^2+2x^2)^2)

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(\partial)/(\partial x)((7y-7x)/(y^2+2x^2))

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

\frac{14 x ^{2} - 28 y x - 7 y ^{2}}{( y ^{2} + 2 x ^{2} ) ^{2}}

Solution steps

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

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

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

\frac{\partial}{\partial x} (y^{2} + 2 x^{2}) = 4 x

= \frac{( - 7 ) ( y ^{2} + 2 x ^{2} ) - 4 x ( 7 y - 7 x )}{( y ^{2} + 2 x ^{2} ) ^{2}}

Simplify

\frac{( - 7 ) ( y ^{2} + 2 x ^{2} ) - 4 x ( 7 y - 7 x )}{( y ^{2} + 2 x ^{2} ) ^{2}} : \frac{14 x ^{2} - 28 y x - 7 y ^{2}}{( y ^{2} + 2 x ^{2} ) ^{2}}

= \frac{14 x ^{2} - 28 y x - 7 y ^{2}}{( y ^{2} + 2 x ^{2} ) ^{2}}

(x^{2} - 2 x - 2 sin (x - 2))^{^{'}}

x \to 2 lim (4 ln (2))

n = 1 \sum \infty \frac{n !}{n !}

\int x cos (n x π) d x

\int \frac{1}{9 e ^{- 8 x} + e ^{8 x}} d x

What is (\partial)/(\partial x)((7y-7x)/(y^2+2x^2)) ?
The answer to (\partial)/(\partial x)((7y-7x)/(y^2+2x^2)) is (14x^2-28yx-7y^2)/((y^2+2x^2)^2)