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})

\int e^{x} - x^{\frac{2}{5}} d x

in v erse l a pl a ce \frac{3}{2 s + 1} \cdot \frac{1}{s}

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

t \to \frac{x}{2} lim (\frac{sin ( t )}{t})

s l o p e (- 3.5) (4.3)