derivative of sqrt(x)e^{2x}

Lösung

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

\frac{e ^{2 x}}{2 x} + 2 e^{2 x} x

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = e^{2 x}

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

= \frac{1}{2 x} e^{2 x} + e^{2 x} \cdot 2 x

\frac{1}{2 x} e^{2 x} = \frac{e ^{2 x}}{2 x}

= \frac{e ^{2 x}}{2 x} + 2 e^{2 x} x

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

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

\frac{d}{d x} (11 x arcsin (x))

\frac{d y}{d x} = \frac{y ^{3}}{e ^{x}}

\frac{\partial}{\partial x} (sec (\frac{x}{2}))