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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

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

\frac{\partial}{\partial x} (2 e^{x^{9} y})

d er i v a t i v e (\frac{x + 9}{x - 9})^{5}

x \to 16 lim (\frac{( 4 - x )}{( 16 x - x ^{2} )})

\int (1 - t^{- 0.52}) d t