derivative of (cos(x)/(x^5))

Lösung

\frac{d}{d x} (\frac{cos ( x )}{x ^{5}})

- \frac{x sin ( x ) + 5 cos ( x )}{x ^{6}}

Schritte zur Lösung

\frac{d}{d x} (\frac{cos ( x )}{x ^{5}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( cos ( x ) ) x ^{5} - \frac{d}{d x} ( x ^{5} ) cos ( x )}{( x ^{5} ) ^{2}}

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{( - sin ( x ) ) x ^{5} - 5 x ^{4} cos ( x )}{( x ^{5} ) ^{2}}

Vereinfache

\frac{( - sin ( x ) ) x ^{5} - 5 x ^{4} cos ( x )}{( x ^{5} ) ^{2}} : - \frac{x sin ( x ) + 5 cos ( x )}{x ^{6}}

= - \frac{x sin ( x ) + 5 cos ( x )}{x ^{6}}

\int sin^{5} (t) cos^{7} (t) d t

\frac{d}{d x} (arctanh (3 x))

d er i v a t i v e ln (\frac{x ^{2}}{2 x ^{2} + 3 x + 2})

\int x - 25 - x^{2} d x

\frac{\partial}{\partial x} (2 x^{4} + 3 y^{3} + 2 x y)