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

Lösung

\frac{d}{d 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}}

\frac{\partial}{\partial x} (\frac{1}{2} (x^{2} + 10 y^{2}))

f (x) = x - cos (x)

\int_{0}^{6} 2. 3^{t} sin (\frac{t}{2}) d t

\int \frac{( 2 x + 4 )}{x ^{2} + 4 x + 5} d x

\int \frac{x ^{2} + 2 x + 3}{x ^{3} + 3 x ^{2} + 9 x + 1} d x