What is the derivative of (xy/(x-y)) ?

The derivative of (xy/(x-y)) is (x^2\frac{dy)/(dx)-y^2}{(x-y)^2}

What is the first derivative of (xy/(x-y)) ?

The first derivative of (xy/(x-y)) is (x^2\frac{dy)/(dx)-y^2}{(x-y)^2}

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\frac{d}{d x} (\frac{x y}{x - y})

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

Solution steps

\frac{d}{d x} (\frac{x y}{x - y})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

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

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

Expand

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

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

\frac{d}{d x} (3 x - \frac{5}{x})

y = \frac{1}{2} x^{2}, 2 x

\frac{d}{d x} (5 cos (2 x))

x \to b lim (\frac{x ^{2}}{2})

\frac{d x}{d y}, x y = 2

What is the derivative of (xy/(x-y)) ?
The derivative of (xy/(x-y)) is (x^2\frac{dy)/(dx)-y^2}{(x-y)^2}
What is the first derivative of (xy/(x-y)) ?
The first derivative of (xy/(x-y)) is (x^2\frac{dy)/(dx)-y^2}{(x-y)^2}