derivative f(x)=(sin(x))/(x^3)

Lösung

ableitung von

f (x) = \frac{sin ( x )}{x ^{3}}

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

x y^{^{'}} + y = 6 x^{2}, y (1) = 2

n \to \infty lim (n^{10})

d er i v a t i v e f (x) = 2 x - x ln ∣ x ∣

n = 0 \sum \infty \frac{1 ^{n}}{2 n + 1}

\frac{d}{d x} (x^{8} sin (x))