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

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

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

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

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

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

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

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

Expand

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

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

x \to 0 lim (- 3 - 2 x)

\int (1 - x^{2})^{- \frac{3}{2}} d x

\frac{d y}{d x} = x^{2} e^{x^{3}} y^{3}

\frac{\partial}{\partial x} (sin (π (3 x - 2 y)))

\frac{d}{d x} (x^{3} - 3 x^{2} + 3 x - 1)

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