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

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

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

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

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

Solution steps

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

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

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

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

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

Simplify

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

2 y

\int_{1}^{2} \frac{4 ln ( x )}{x ^{2}} d x

\frac{d}{d x} (\frac{e ^{x} - e ^{- x}}{2})

\frac{\partial}{\partial x} (cos (y^{3} - 6 x))

e^{- \frac{x}{2}}

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