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

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

Popular >

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

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

\frac{\partial}{\partial x} ((4 - x^{2} - y^{2})^{\frac{1}{2}})

\frac{d}{d t} (\frac{1}{t ^{2} - 2})

\frac{\partial}{\partial x} (ln (4 + 3 x^{2} + 2 y^{2}))

f (x) = 2 sin^{4} (x)

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