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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

x \to \infty lim (- 1)

x \to 4 lim (2 x)

2 x^{2}, x^{4} - 2 x^{2}

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

\frac{d}{d x} (\frac{x + 1}{x ^{2} + 1})

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