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Beliebt Rechnen >

derivative (cos(x))/(x^9)

Lösung

ableitung von

\frac{cos ( x )}{x ^{9}}

Lösung

- \frac{x sin ( x ) + 9 cos ( x )}{x ^{10}}

Schritte zur Lösung

\frac{d}{d x} (\frac{cos ( x )}{x ^{9}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( cos ( x ) ) x ^{9} - \frac{d}{d x} ( x ^{9} ) cos ( x )}{( x ^{9} ) ^{2}}

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

\frac{d}{d x} (x^{9}) = 9 x^{8}

= \frac{( - sin ( x ) ) x ^{9} - 9 x ^{8} cos ( x )}{( x ^{9} ) ^{2}}

Vereinfache

\frac{( - sin ( x ) ) x ^{9} - 9 x ^{8} cos ( x )}{( x ^{9} ) ^{2}} : - \frac{x sin ( x ) + 9 cos ( x )}{x ^{10}}

= - \frac{x sin ( x ) + 9 cos ( x )}{x ^{10}}

Graph

Beliebte Beispiele

integral of 1/(u^2-u)

\int \frac{1}{u ^{2} - u} d u

limit as x approaches-2 of (x^3-8)/(x-2)

x \to - 2 lim (\frac{x ^{3} - 8}{x - 2})

(\partial)/(\partial y)(x^2+4y)

\frac{\partial}{\partial y} (x^{2} + 4 y)

steigung (7,-5),(-2,-5)

s l o p e (7, - 5), (- 2, - 5)

y = 5^{6 x^{2}}