derivative of 2xe^{2x}+2x^2e^{2x}

Lösung

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

2 e^{2 x} + 8 e^{2 x} x + 4 e^{2 x} x^{2}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

2 (e^{2 x} + 2 e^{2 x} x) + 2 (2 x e^{2 x} + e^{2 x} \cdot 2 x^{2}) : 2 e^{2 x} + 8 e^{2 x} x + 4 e^{2 x} x^{2}

= 2 e^{2 x} + 8 e^{2 x} x + 4 e^{2 x} x^{2}

\int a sin (x) d x

\frac{d}{d x} (cos (x^{2} + y^{2}))

a re a y^{2} = 4 x, y = 2 x + 4

y^{^{''}} + 9 y = - 30 sin (3 t)

\frac{d}{d x} (ln (sec (x) - tan (x)))