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

The answer to (\partial)/(\partial x)((x-2y)/(x+2)) is (2y+2)/((x+2)^2)

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

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

\frac{2 y + 2}{( x + 2 ) ^{2}}

Solution steps

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

\frac{\partial}{\partial x} (x - 2 y) = 1

\frac{\partial}{\partial x} (x + 2) = 1

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

Simplify

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

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

n = 1 \sum \infty \frac{4 n}{7 n + 1}

n = 1 \sum \infty 2^{n - 1}

\int_{0}^{\frac{π}{6}} (1 - cos (3 x)) sin (3 x) d x

4 e^{2 x}

\frac{d}{d x} (3 x^{2} + 1)

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