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

Soluzione

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

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

Fasi della soluzione

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

Applica la regola del quoziente:

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

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

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

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

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

Semplificare

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

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

\int_{y}^{x} \frac{e ^{t}}{t} d t

(32) (41.5)

\frac{\partial}{\partial x} (\frac{x}{x ^{4} - y ^{6}})

\int cos^{2} (x) tan^{3} (x) d x

f (x) = \frac{e ^{x}}{x ^{2}}