derivative of ar(xcos(x))

Lösung

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

a (cos (x) \frac{d}{d x} (r (x)) - sin (x) r (x))

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= a \frac{d}{d x} (r (x) cos (x))

Wende die Produktregel an:

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

f = r (x), g = cos (x)

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

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

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

Vereinfache

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

\int \frac{- x - 1}{x ^{2} + 3} d x

\int x x^{\frac{3}{2}} - 1 d x

a re a sin (x), cos (x), x = - \frac{π}{6}

\frac{d}{d x} (x^{2} e^{5 x})

d er i v a t i v e 7 + 4 x