derivative of Axe^{x/2}+B

Lösung

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

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

Schritte zur Lösung

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

Behandle

A, B

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d B}{d x} = 0

= A (e^{\frac{x}{2}} + \frac{e ^{\frac{x}{2}} x}{2}) + 0

Vereinfache

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

\frac{d}{d x} (\frac{3 x - 2}{2 x + 1})

x \to 3 - lim (\frac{2 - x}{x - 3})

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

\int \frac{7}{( 7 ^{2} + x ^{2} ) ^{\frac{3}{2}}} d x

x \to 0 lim (x [\frac{1}{x}])