derivative x^3e^xcos(x)

Lösung

ableitung von

x^{3} e^{x} cos (x)

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

\int \frac{2 x + 4}{x ^{2} - 2 x - 3} d x

\int 3 x^{3} + 4 x^{2} - 2 x^{- 1} + 13 d x

\int - y^{3} d y

\frac{d}{d x} (2 e^{x} - 5 cos (x) + 3)

d er i v a t i v e 4 e^{x} + \frac{4}{3 x}