derivative of e^{2x}-x^2-1

Lösung

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

- 2 x + 2 e^{2 x}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{d}{d x} (1) = 0

= e^{2 x} \cdot 2 - 2 x - 0

Vereinfache

= - 2 x + 2 e^{2 x}