derivative derivative of xcos(x)

Lösung

ableitung von

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

cos (x) - x sin (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = cos (x)

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

\frac{d x}{d x} = 1

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

= 1 \cdot cos (x) + (- sin (x)) x

Vereinfache

= cos (x) - x sin (x)

d er i v a t i v e \frac{d}{d x} (cos (x) sec (x))

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

s l o p e (4, 0), (0, 3)

l o n g d i v i s i o n x \to \infty lim (\frac{x}{4})

\frac{d y}{d x} y = cos (x)