derivative f(x)=3x^2e^x+e^x(x^3+1)

Lösung

ableitung von

f (x) = 3 x^{2} e^{x} + e^{x} (x^{3} + 1)

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

Schritte zur Lösung

\frac{d}{d x} (3 x^{2} e^{x} + e^{x} (x^{3} + 1))

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} + 1))

\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} + 1)) = e^{x} (x^{3} + 1) + 3 x^{2} e^{x}

= 3 (2 x e^{x} + e^{x} x^{2}) + e^{x} (x^{3} + 1) + 3 x^{2} e^{x}

Vereinfache

3 (2 x e^{x} + e^{x} x^{2}) + e^{x} (x^{3} + 1) + 3 x^{2} e^{x} : e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x + e^{x}

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

y^{^{'}} = 18.2 - 0.7 y

x \to 4 lim (x)

in v erse l a pl a ce \frac{s + 3}{( s + 3 ) ^{2} + 4}

\frac{d}{d x} (\frac{1}{2} cos (\frac{x}{2}))

y^{^{'}} = y^{2} + y