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Beliebt Rechnen >

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

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (x e^{3 x^{2}}) = e^{3 x^{2}} + 6 e^{3 x^{2}} x^{2}

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

= e^{3 x^{2}} + 6 e^{3 x^{2}} x^{2} + 0

Vereinfache

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

Graph

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