derivative of sqrt(xe^{2x)}

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{2 x e ^{2 x}} \frac{d}{d x} (x e^{2 x})

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

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

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

Vereinfache

\frac{1}{2 x e ^{2 x}} (e^{2 x} + 2 e^{2 x} x) : \frac{e ^{x} ( 1 + 2 x )}{2 x}

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

\int sin^{2} (\frac{π}{4} + \frac{t}{2}) d t

x \to - 7 lim (x^{2} - 49)

d er i v a t i v e \frac{1}{t ^{2} + 5 t - 1}

t an g e n t y = \frac{4 x}{x ^{2} + 1}, (- 1, - 2)

a re a x^{3} - 13 x^{2} + 30 x, - x^{3} + 13 x^{2} - 30 x