derivative of (xcos(x-sin(x))/(x^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

x \to 3 lim (10 (x + 3))

d er i v a t i v e f (x) = 6 x^{2} - 5 x

n = 0 \sum \infty \frac{1}{n ^{\frac{1}{n}}}

d er i v a t i v e 9 arctan (x + 1 + x^{2})

x \to 0 lim (4 - x)