derivative of c_{1}e^x+c_{2}xe^x

Lösung

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

c_{1} e^{x} + c_{2} (e^{x} + e^{x} x)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= c_{1} e^{x} + c_{2} (e^{x} + e^{x} x)

n = 0 \sum \infty \frac{1}{1 0 ^{n}}

y^{^{'}} + 7 y = t + e^{- 2 t}

x \to 0 + lim (x^{3} + 3 x + 2)

\int \frac{2}{x ^{2} + 2 x + 2} d x

x \to 1 lim (\frac{x - 1}{x ^{2} - 1})