derivative of x^3cos(x-x^3sin(x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

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

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

x \to 2 lim (\frac{x ^{2}}{2 x - 4})

\frac{\partial}{\partial x} (\frac{x y}{x - y})

\frac{d}{d x} (450 x - 90 x^{2})

\int - sin (y) d y

in v erse l a pl a ce \frac{2 s + 1}{s ( s + 1 )}