derivative of x^2sin(x+2xcos(x))

Lösung

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

x^{2} cos (x) + 2 cos (x)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Vereinfache

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

= x^{2} cos (x) + 2 cos (x)

\frac{d y}{d x} = \frac{2 y}{2 x + 1}, y (0) = e

\int_{0}^{4} x e^{x^{2}} d x

\int_{0}^{a} x x^{2} + a^{2} d x

\frac{d}{d x} (sin (2) (x))

d er i v a t i v e - \frac{y}{x + e ^{y}}