What is (\partial)/(\partial x)((2x-y)/(x+4y)) ?

The answer to (\partial)/(\partial x)((2x-y)/(x+4y)) is (9y)/((x+4y)^2)

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(\partial)/(\partial x)((2x-y)/(x+4y))

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

\frac{9 y}{( x + 4 y ) ^{2}}

Solution steps

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

\frac{\partial}{\partial x} (2 x - y) = 2

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

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

Simplify

\frac{2 ( x + 4 y ) - 1 \cdot ( 2 x - y )}{( x + 4 y ) ^{2}} : \frac{9 y}{( x + 4 y ) ^{2}}

= \frac{9 y}{( x + 4 y ) ^{2}}

\int e^{c o s (t)} d t

(x - 3)^{- 2}

\frac{d y}{d x} = \frac{e ^{x}}{y ^{2}}

\int \frac{x ^{2}}{e ^{x}} d x

\int tan^{6} (x) d x

What is (\partial)/(\partial x)((2x-y)/(x+4y)) ?
The answer to (\partial)/(\partial x)((2x-y)/(x+4y)) is (9y)/((x+4y)^2)