derivative of (x+pi/x cos(x))

Lösung

\frac{d}{d x} (\frac{x + π}{x} cos (x))

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x + π}{x} cos (x))

Wende die Produktregel an:

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

f = \frac{x + π}{x}, g = cos (x)

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

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

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

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

Vereinfache

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

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

\int 2^{7 - x} d x

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d er i v a t i v e ln (x^{2} - 7)

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\frac{d}{d x} f (x) = x^{2} + 8 x + 7