derivative of e^xcos(x-x^3sin(x)+pi)

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{d π}{d x} = 0

= e^{x} cos (x) - e^{x} sin (x) - (3 x^{2} sin (x) + cos (x) x^{3}) + 0

Vereinfache

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

y^{^{'}} = \frac{y}{50} 5, y (0) = 30

s l o p e (7, 6), (- 7, - 7)

\frac{d y}{d x} = \frac{y}{x} + (\frac{y}{x})^{2} - 1

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{1 + e ^{t}}

\int x 1 + x + \frac{x ^{2} + 4}{x - 1} d x