de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of (cos(x)/(x^7))

Lösung

\frac{d}{d x} (\frac{cos ( x )}{x ^{7}})

Lösung

- \frac{x sin ( x ) + 7 cos ( x )}{x ^{8}}

Schritte zur Lösung

\frac{d}{d x} (\frac{cos ( x )}{x ^{7}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( cos ( x ) ) x ^{7} - \frac{d}{d x} ( x ^{7} ) cos ( x )}{( x ^{7} ) ^{2}}

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

\frac{d}{d x} (x^{7}) = 7 x^{6}

= \frac{( - sin ( x ) ) x ^{7} - 7 x ^{6} cos ( x )}{( x ^{7} ) ^{2}}

Vereinfache

\frac{( - sin ( x ) ) x ^{7} - 7 x ^{6} cos ( x )}{( x ^{7} ) ^{2}} : - \frac{x sin ( x ) + 7 cos ( x )}{x ^{8}}

= - \frac{x sin ( x ) + 7 cos ( x )}{x ^{8}}

Graph

Beliebte Beispiele

derivative of (5x-4^3)

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

integral of sqrt(x-4)

\int x - 4 d x

integral of e^{-x}*x^{-1}

\int e^{- x} \cdot x^{- 1} d x

derivative of 1/(sqrt(9+x^2))

\frac{d}{d x} (\frac{1}{9 + x ^{2}})

derivative of xye^{xy}

\frac{d}{d x} (x y e^{x y})