derivative of (x+y/(x-y))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\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}}

Multipliziere aus

(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}}

t an g e n t 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