derivative y=(x-4)/x

Lösung

ableitung von

y = \frac{x - 4}{x}

\frac{4}{x ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x - 4 ) x - \frac{d x}{d x} ( x - 4 )}{x ^{2}}

\frac{d}{d x} (x - 4) = 1

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

= \frac{1 \cdot x - 1 \cdot ( x - 4 )}{x ^{2}}

Vereinfache

\frac{1 \cdot x - 1 \cdot ( x - 4 )}{x ^{2}} : \frac{4}{x ^{2}}

= \frac{4}{x ^{2}}

x \to - 10 lim (f (x))

x \to 3 - lim (\frac{x + 3}{x ^{2} - 9})

\int \frac{4}{e ^{t}} d t

\int \frac{1}{4 sin ( x ) + 3 cos ( x )} d x

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