What is (\partial)/(\partial y)(y/(y+4x)) ?

The answer to (\partial)/(\partial y)(y/(y+4x)) is (4x)/((y+4x)^2)

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(\partial)/(\partial y)(y/(y+4x))

\frac{\partial}{\partial y} (\frac{y}{y + 4 x})

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

Solution steps

\frac{\partial}{\partial y} (\frac{y}{y + 4 x})

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

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

\frac{\partial}{\partial y} (y + 4 x) = 1

= \frac{1 \cdot ( y + 4 x ) - 1 \cdot y}{( y + 4 x ) ^{2}}

1 \cdot (y + 4 x) - 1 \cdot y = 4 x

= \frac{4 x}{( y + 4 x ) ^{2}}

\frac{d}{d x} (\frac{2 e ^{x}}{5 x})

\frac{d y}{d t} + e^{t} y = 22 e^{t}

\int sin (2 θ) cos^{4} (2 θ) d θ

\int \frac{1}{sec ( θ )} d θ

\frac{d}{d t} (t cos (t))

What is (\partial)/(\partial y)(y/(y+4x)) ?
The answer to (\partial)/(\partial y)(y/(y+4x)) is (4x)/((y+4x)^2)