derivative (cos(x))/(x^4)

Lösung

ableitung von

\frac{cos ( x )}{x ^{4}}

- \frac{x sin ( x ) + 4 cos ( x )}{x ^{5}}

Schritte zur Lösung

\frac{d}{d x} (\frac{cos ( x )}{x ^{4}})

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

Vereinfache

\frac{( - sin ( x ) ) x ^{4} - 4 x ^{3} cos ( x )}{( x ^{4} ) ^{2}} : - \frac{x sin ( x ) + 4 cos ( x )}{x ^{5}}

= - \frac{x sin ( x ) + 4 cos ( x )}{x ^{5}}

\frac{d}{d x} (5 x + 7)

d er i v a t i v e \frac{ln ( x )}{x}

\int_{0}^{1} x 3 1 - x d x

\int \frac{1}{( 1 + e ^{- x} )} d x

\frac{\partial}{\partial x} (sin (\frac{x}{2}))