derivative of-x^2sin(x+4xcos(x)+2sin(x))

Lösung

\frac{d}{d x} (- x^{2} sin (x) + 4 x cos (x) + 2 sin (x))

- x^{2} cos (x) - 6 x sin (x) + 6 cos (x)

Schritte zur Lösung

\frac{d}{d x} (- x^{2} sin (x) + 4 x cos (x) + 2 sin (x))

Wende die Summen-/Differenzregel an:

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

= - \frac{d}{d x} (x^{2} sin (x)) + \frac{d}{d x} (4 x cos (x)) + \frac{d}{d x} (2 sin (x))

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

\frac{d}{d x} (4 x cos (x)) = 4 (cos (x) - x sin (x))

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

= - (2 x sin (x) + cos (x) x^{2}) + 4 (cos (x) - x sin (x)) + 2 cos (x)

Vereinfache

- (2 x sin (x) + cos (x) x^{2}) + 4 (cos (x) - x sin (x)) + 2 cos (x) : - x^{2} cos (x) - 6 x sin (x) + 6 cos (x)

= - x^{2} cos (x) - 6 x sin (x) + 6 cos (x)

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

\frac{d}{d x} (6 x^{2} + 8 x + 6)

\int x^{15} e^{- x^{8}} d x

\int (2 x + 5) (x^{2} + 5 x)^{7} d x

\frac{d y}{d x} = \frac{13 x y}{( ln ( y ) ) ^{10}}