derivative f(x)=3x^2e^x+e^x(x^3+5)

Lösung

ableitung von

f (x) = 3 x^{2} e^{x} + e^{x} (x^{3} + 5)

e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 5 e^{x}

Schritte zur Lösung

\frac{d}{d x} (3 x^{2} e^{x} + e^{x} (x^{3} + 5))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (3 x^{2} e^{x}) + \frac{d}{d x} (e^{x} (x^{3} + 5))

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

\frac{d}{d x} (e^{x} (x^{3} + 5)) = e^{x} (x^{3} + 5) + 3 x^{2} e^{x}

= 3 (2 x e^{x} + e^{x} x^{2}) + e^{x} (x^{3} + 5) + 3 x^{2} e^{x}

Vereinfache

3 (2 x e^{x} + e^{x} x^{2}) + e^{x} (x^{3} + 5) + 3 x^{2} e^{x} : e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 5 e^{x}

= e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + 5 e^{x}

\frac{1}{3} \frac{d x}{d t} - 2 e^{- t} = - x

\int_{l n (8)}^{l n (64)} e^{\frac{x}{3}} d x

x \to 0 + lim (x - x)

\int x + \frac{1}{2 x} d x

\frac{d y}{d x} = (x - 5) e^{- 2 y}