derivative 1/x cos(x)

Lösung

ableitung von

\frac{1}{x} cos (x)

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

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x} cos (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{1}{x}, g = cos (x)

= \frac{d}{d x} (\frac{1}{x}) cos (x) + \frac{d}{d x} (cos (x)) \frac{1}{x}

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

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

= (- \frac{1}{x ^{2}}) cos (x) + (- sin (x)) \frac{1}{x}

Vereinfache

(- \frac{1}{x ^{2}}) cos (x) + (- sin (x)) \frac{1}{x} : - \frac{cos ( x )}{x ^{2}} - \frac{sin ( x )}{x}

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

in v erse l a pl a ce \frac{s + 5}{7 s ^{2} + 26 s + 25}

\frac{d y}{d t} + 4 y = 0

t an g e n t f (x) = x^{7}, at x = 2

\frac{d v}{d t} = - k t v^{2}, v (0) = 50

l a pl a ce t r an s f or m sin (3 x)