derivative of ax^2e^{2x}

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

x \to + 8 - lim (\frac{x}{x - 8})

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

t an g e n t f (x) = \frac{3}{x}, (1, 3)

y^{^{''}} + 3 y^{^{'}} - 10 y = x (e^{x} + 1)

\frac{d}{d x} (3^{- 6 x + 6})