derivative f(x)=9e^xcos(x)

Lösung

ableitung von

f (x) = 9 e^{x} cos (x)

9 (e^{x} cos (x) - e^{x} sin (x))

Schritte zur Lösung

\frac{d}{d x} (9 e^{x} cos (x))

Entferne die Konstante:

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

= 9 \frac{d}{d x} (e^{x} cos (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = cos (x)

= 9 (\frac{d}{d x} (e^{x}) cos (x) + \frac{d}{d x} (cos (x)) e^{x})

\frac{d}{d x} (e^{x}) = e^{x}

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

= 9 (e^{x} cos (x) + (- sin (x)) e^{x})

Vereinfache

= 9 (e^{x} cos (x) - e^{x} sin (x))

\int sin (x) (cos (2 x)) d x

n = 1 \sum \infty \frac{1}{1 + 4 ^{n}}

n = 0 \sum \infty a^{n}

\frac{d}{d x} ((5 x^{3} - 2 x^{2}) (6 x^{3}))

\frac{d}{d x} (1 - \frac{x ^{2}}{16})