derivative of 2x^2cos(3x)

Lösung

\frac{d}{d x} (2 x^{2} cos (3 x))

2 (2 x cos (3 x) - 3 x^{2} sin (3 x))

Schritte zur Lösung

\frac{d}{d x} (2 x^{2} cos (3 x))

Entferne die Konstante:

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

= 2 \frac{d}{d x} (x^{2} cos (3 x))

Wende die Produktregel an:

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

f = x^{2}, g = cos (3 x)

= 2 (\frac{d}{d x} (x^{2}) cos (3 x) + \frac{d}{d x} (cos (3 x)) x^{2})

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

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= 2 (2 x cos (3 x) + (- sin (3 x) \cdot 3) x^{2})

Vereinfache

= 2 (2 x cos (3 x) - 3 x^{2} sin (3 x))

\int arccot (13 y) d y

\int 1 + cos (8 x) d x

\frac{d}{d x} (cos (arctan (5 x)))

n = 0 \sum \infty n^{n} (x - 3)^{n}

x \to 2 lim (\frac{3}{x + 2})