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^2))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

limit as x approaches-6 of-12

x \to - 6 lim (- 12)

d/(dθ)(1-cos(θ))

\frac{d}{d θ} (1 - cos (θ))

integral of 1/(x(x-3))

\int \frac{1}{x ( x - 3 )} d x

derivative f(x)=10x^3

d er i v a t i v e f (x) = 10 x^{3}

integral of ((ln(x))^{34})/x

\int \frac{( ln ( x ) ) ^{34}}{x} d x