What is (\partial)/(\partial x)((5xy)/(x-y)) ?

The answer to (\partial)/(\partial x)((5xy)/(x-y)) is -(5y^2)/((x-y)^2)

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(\partial)/(\partial x)((5xy)/(x-y))

\frac{\partial}{\partial x} (\frac{5 x y}{x - y})

- \frac{5 y ^{2}}{( x - y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{5 x y}{x - y})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 y \frac{\partial}{\partial x} (\frac{x}{x - y})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 5 y \frac{\frac{\partial}{\partial x} ( x ) ( x - y ) - \frac{\partial}{\partial x} ( x - y ) x}{( x - y ) ^{2}}

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

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

= 5 y \frac{1 \cdot ( x - y ) - 1 \cdot x}{( x - y ) ^{2}}

Simplify

5 y \frac{1 \cdot ( x - y ) - 1 \cdot x}{( x - y ) ^{2}} : - \frac{5 y ^{2}}{( x - y ) ^{2}}

= - \frac{5 y ^{2}}{( x - y ) ^{2}}

f (x) = \frac{6 x}{( 5 - 2 x ) ^{4}}, at x = 1

x 1 + y^{2} d x = d y

\frac{d}{d x} (\frac{ln ( x )}{5 x ^{3}})

\int 7 x sec^{2} (x) d x

10000 - 9000 e^{- 0.3 t}

What is (\partial)/(\partial x)((5xy)/(x-y)) ?
The answer to (\partial)/(\partial x)((5xy)/(x-y)) is -(5y^2)/((x-y)^2)