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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

d er i v a t i v e (3 x^{3} + 2 x) (x - 2) (x + 4)

cos (x) d x - sin (y) d y = 0

\int arcsin (d) x d x

n \to \infty lim (1 - n)

\int (- \frac{3 x ^{2}}{5}) d x