What is (\partial)/(\partial x)(x/(1+2x+3y)) ?

The answer to (\partial)/(\partial x)(x/(1+2x+3y)) is (3y+1)/((1+2x+3y)^2)

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(\partial)/(\partial x)(x/(1+2x+3y))

\frac{\partial}{\partial x} (\frac{x}{1 + 2 x + 3 y})

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

Solution steps

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

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

\frac{\partial}{\partial x} (1 + 2 x + 3 y) = 2

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

Simplify

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

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What is (\partial)/(\partial x)(x/(1+2x+3y)) ?
The answer to (\partial)/(\partial x)(x/(1+2x+3y)) is (3y+1)/((1+2x+3y)^2)