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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

\frac{( - 1 ) ( x + 2 y ) - 2 ( x - y )}{( x + 2 y ) ^{2}} : - \frac{3 x}{( x + 2 y ) ^{2}}

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

t a y l or cos (x) - x^{2}, 1

\int_{1}^{6} \frac{7 ln ( x )}{x ^{2}} d x

x \to 8 lim (2 x - 3)

\int_{1}^{3} 4 r^{4} ln (r) d r

d er i v a t i v e 2^{x^{2} + x}

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