derivative of e^{5x}cos(3x)

Lösung

\frac{d}{d x} (e^{5 x} cos (3 x))

5 e^{5 x} cos (3 x) - 3 e^{5 x} sin (3 x)

Schritte zur Lösung

\frac{d}{d x} (e^{5 x} cos (3 x))

Wende die Produktregel an:

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

f = e^{5 x}, g = cos (3 x)

= \frac{d}{d x} (e^{5 x}) cos (3 x) + \frac{d}{d x} (cos (3 x)) e^{5 x}

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

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

= e^{5 x} \cdot 5 cos (3 x) + (- sin (3 x) \cdot 3) e^{5 x}

Vereinfache

= 5 e^{5 x} cos (3 x) - 3 e^{5 x} sin (3 x)

\frac{d}{d x} (\frac{x ^{4}}{3 - x ^{3}})

\frac{d}{d x} (- 4 e^{- 4 x})

\frac{d}{d x} (7 x - 8)

n = 0 \sum \infty (400) (0.1)^{n}

\frac{d y}{d x} = \frac{x ^{2} + 2}{3 y ^{2}}