derivative of a(e^x+e^{xx})

Lösung

\frac{d}{d x} (a (e^{x} + e^{xx}))

a (e^{x} + e^{x^{2}} \cdot 2 x)

Schritte zur Lösung

\frac{d}{d x} (a (e^{x} + e^{xx}))

Vereinfache

a (e^{x} + e^{xx}) : a (e^{x} + e^{x^{2}})

= \frac{d}{d x} (a (e^{x} + e^{x^{2}}))

Entferne die Konstante:

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

= a \frac{d}{d x} (e^{x} + e^{x^{2}})

Wende die Summen-/Differenzregel an:

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

= a (\frac{d}{d x} (e^{x}) + \frac{d}{d x} (e^{x^{2}}))

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

\frac{d}{d x} (e^{x^{2}}) = e^{x^{2}} \cdot 2 x

= a (e^{x} + e^{x^{2}} \cdot 2 x)

d er i v a t i v e f (x) = \frac{1}{x + 1}

x \to \infty lim (y^{- x})

x \to 2 lim (5)

a re a e^{- x}, 0, 0, ln (3)

\frac{d y}{d t} = 6 y + 2 t - 4, y (0) = 3