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}}

f (x) = x^{4} - 18 x^{2} + 81, at x = 1

\frac{\partial}{\partial x} (2 y^{3} x)

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

\frac{d}{d x} (\frac{17}{x})

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

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}