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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

x \to 5 lim (2 x^{2} - 7 x + 13)

\int \frac{e ^{8 s i n (x)}}{sec ( x )} d x

\int (2 - e^{- x})^{2} d x

(x csc (\frac{y}{x}) - y) d x + x d y = 0

x \to - 2 lim (\frac{6}{x + 2})