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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

\frac{d}{d x} (- \frac{81}{x ^{4}})

\int 1 + 6 x^{\frac{1}{2}} d x

f (x) = x \cdot sin (x)

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (1) = 0, y^{^{'}} (1) = 3

f^{^{'}} (x) = x^{2} - x

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