What is (\partial)/(\partial x)(x/(x+3y)) ?

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

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(\partial)/(\partial x)(x/(x+3y))

\frac{\partial}{\partial x} (\frac{x}{x + 3 y})

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

Solution steps

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

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

\frac{\partial}{\partial x} (x + 3 y) = 1

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

1 \cdot (x + 3 y) - 1 \cdot x = 3 y

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

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