derivative of ((e^x-1)/x)

Lösung

\frac{d}{d x} (\frac{( e ^{x} - 1 )}{x})

\frac{e ^{x} x - e ^{x} + 1}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( e ^{x} - 1 )}{x})

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (e^{x} - 1) = e^{x}

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

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

Vereinfache

= \frac{e ^{x} x - e ^{x} + 1}{x ^{2}}

\frac{d}{d x} (e^{s i n^{2} (x)})

a re a y = \frac{2}{x}, y = 8 x, y = \frac{1}{2} x

\frac{d}{d x} (\frac{3}{4 ( 2 x - 5 ) ^{8}})

x \to - \infty lim (\frac{x ^{2} + 8 x}{8 x + 1})

d er i v a t i v e f (x) = 2000 (x^{2} + 5)^{\frac{1}{3}}