derivative of (x-y/x)

Lösung

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

\frac{- x \frac{d y}{d x} + y}{x ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

d er i v a t i v e y = 2 cos (2 x)

d er i v a t i v e (x + 1)^{l n (x)}

\int \frac{x ^{2}}{16 - 25 x ^{2}} d x

\int \frac{( 16 x )}{( x ^{2} - 9 ) ^{5}} d x

t an g e n t x^{2} - \frac{x}{5}