derivative of 5(e^xcos(x-e^xsin(x)))

Lösung

\frac{d}{d x} (5 (e^{x} cos (x) - e^{x} sin (x)))

- 10 e^{x} sin (x)

Schritte zur Lösung

\frac{d}{d x} (5 (e^{x} cos (x) - e^{x} sin (x)))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (e^{x} cos (x) - e^{x} sin (x))

Wende die Summen-/Differenzregel an:

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

= 5 (\frac{d}{d x} (e^{x} cos (x)) - \frac{d}{d x} (e^{x} sin (x)))

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

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

= 5 (e^{x} cos (x) - e^{x} sin (x) - (e^{x} sin (x) + cos (x) e^{x}))

Vereinfache

5 (e^{x} cos (x) - e^{x} sin (x) - (e^{x} sin (x) + cos (x) e^{x})) : - 10 e^{x} sin (x)

= - 10 e^{x} sin (x)

\int x 6 - x d x

x \to 3 lim (\frac{x - 1}{x ^{2} - 1})

in v erse l a pl a ce e^{- 2 s} \frac{1}{s - 9}

\int \frac{1}{1 + x} d x

s l o p e (0, - 6), (3, - 5)