derivative of (cos(x-1)/x)

Lösung

\frac{d}{d x} (\frac{cos ( x ) - 1}{x})

\frac{- x sin ( x ) - cos ( x ) + 1}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{cos ( x ) - 1}{x})

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (cos (x) - 1) = - sin (x)

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

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

Vereinfache

\frac{( - sin ( x ) ) x - 1 \cdot ( cos ( x ) - 1 )}{x ^{2}} : \frac{- x sin ( x ) - cos ( x ) + 1}{x ^{2}}

= \frac{- x sin ( x ) - cos ( x ) + 1}{x ^{2}}

\int_{1}^{3} \frac{5}{x ^{2} + 2 x + 1} d x

\int \frac{1}{200 - x} d x

d er i v a t i v e sin^{2} (e^{s i n^{2} (t)})

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

\frac{d}{d x} ((6 x + 5)^{x})