derivative of (e^{2x}+e^{4x}/3)

Lösung

\frac{d}{d x} (\frac{e ^{2 x} + e ^{4 x}}{3})

\frac{1}{3} (e^{2 x} \cdot 2 + e^{4 x} \cdot 4)

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{2 x} + e ^{4 x}}{3})

Entferne die Konstante:

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

= \frac{1}{3} \frac{d}{d x} (e^{2 x} + e^{4 x})

Wende die Summen-/Differenzregel an:

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

= \frac{1}{3} (\frac{d}{d x} (e^{2 x}) + \frac{d}{d x} (e^{4 x}))

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

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

= \frac{1}{3} (e^{2 x} \cdot 2 + e^{4 x} \cdot 4)

d er i v a t i v e f (q) = \frac{500}{q ^{2}}

x \to 4 lim (\frac{x + 1}{x - 3})

\int (x^{2} - 3 x) d x

\frac{\partial}{\partial x} (e^{x^{2} + y^{2}})

\int_{0}^{2} \frac{2}{8 - x ^{2}} d x