derivative of (cos(x-1)/(x^2))

Lösung

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

- \frac{x sin ( x ) + 2 ( cos ( x ) - 1 )}{x ^{3}}

Schritte zur Lösung

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

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

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

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

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

Vereinfache

\frac{( - sin ( x ) ) x ^{2} - 2 x ( cos ( x ) - 1 )}{( x ^{2} ) ^{2}} : - \frac{x sin ( x ) + 2 ( cos ( x ) - 1 )}{x ^{3}}

= - \frac{x sin ( x ) + 2 ( cos ( x ) - 1 )}{x ^{3}}

\int_{2}^{4} (2 + u)^{2} d u

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

\int (5 cos (3 x) - 4 sin (5 x)) d x

n = 5 \sum \infty \frac{5 ^{n}}{1 2 ^{n}}

x \to \infty lim (\frac{9}{x} - 1)