derivative of (sin(1/x)/(x^2))

Lösung

\frac{d}{d x} (\frac{sin ( \frac{1}{x} )}{x ^{2}})

\frac{- cos ( \frac{1}{x} ) - 2 x sin ( \frac{1}{x} )}{x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{sin ( \frac{1}{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 ( \frac{1}{x} ) ) x ^{2} - \frac{d}{d x} ( x ^{2} ) sin ( \frac{1}{x} )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (sin (\frac{1}{x})) = - \frac{cos ( \frac{1}{x} )}{x ^{2}}

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

= \frac{( - \frac{c o s ( \frac{1}{x} )}{x ^{2}} ) x ^{2} - 2 x sin ( \frac{1}{x} )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{( - \frac{c o s ( \frac{1}{x} )}{x ^{2}} ) x ^{2} - 2 x sin ( \frac{1}{x} )}{( x ^{2} ) ^{2}} : \frac{- cos ( \frac{1}{x} ) - 2 x sin ( \frac{1}{x} )}{x ^{4}}

= \frac{- cos ( \frac{1}{x} ) - 2 x sin ( \frac{1}{x} )}{x ^{4}}

x \to - \infty lim (9)

\int (4 - 3 x)^{5} d x

in v erse l a pl a ce \frac{4}{5 s + 1}

\int ln ∣ 1 + x ∣ d x

\frac{d y}{d x} = e^{- x}