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Beliebt Rechnen >

derivative of (cos(x)/(x^6))

Lösung

\frac{d}{d x} (\frac{cos ( x )}{x ^{6}})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{cos ( x )}{x ^{6}})

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (x^{6}) = 6 x^{5}

= \frac{( - sin ( x ) ) x ^{6} - 6 x ^{5} cos ( x )}{( x ^{6} ) ^{2}}

Vereinfache

\frac{( - sin ( x ) ) x ^{6} - 6 x ^{5} cos ( x )}{( x ^{6} ) ^{2}} : - \frac{x sin ( x ) + 6 cos ( x )}{x ^{7}}

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

Graph

Beliebte Beispiele

t a y l or \frac{1}{2 - x}

integral of (1+x+e^x)

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

f(z)=tan(e^{-6z})

f (z) = tan (e^{- 6 z})

derivative of sin^4(2x+3)

\frac{d}{d x} (sin^{4} (2 x + 3))

derivative (1/x)^3

d er i v a t i v e (\frac{1}{x})^{3}