derivative of (cos(x)/(x^3))

Lösung

\frac{d}{d x} (\frac{cos ( x )}{x ^{3}})

- \frac{x sin ( x ) + 3 cos ( x )}{x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{cos ( x )}{x ^{3}})

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

Vereinfache

\frac{( - sin ( x ) ) x ^{3} - 3 x ^{2} cos ( x )}{( x ^{3} ) ^{2}} : - \frac{x sin ( x ) + 3 cos ( x )}{x ^{4}}

= - \frac{x sin ( x ) + 3 cos ( x )}{x ^{4}}

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

y^{^{''}} + 4 y = sec (2 x)

\frac{d}{d x} (- \frac{15}{16 x ^{\frac{7}{2}}})

x \to 0 lim (\frac{sin ^{3} ( x )}{x})

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