derivative of ae^xcos(x)

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

= a \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)

= a (\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)

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

Vereinfache

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

\frac{\partial}{\partial x} (\frac{( 3 x - 3 z )}{y + 3 z})

\int 3 cos (x) - 2 sin (x) d x

t an g e n t e^{x} + 1, at x = 0

a re a y = 3 + 2 x, y = \frac{9 + x}{3}

t an g e n t y = - 2 x^{3}, (- 2, 16)