d/(dy)(y^2e^{xy^2}+4x^3)

Lösung

\frac{d}{d y} (y^{2} e^{x y^{2}} + 4 x^{3})

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

Schritte zur Lösung

\frac{d}{d y} (y^{2} e^{x y^{2}} + 4 x^{3})

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d y} (y^{2} e^{x y^{2}}) + \frac{d}{d y} (4 x^{3})

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

\frac{d}{d y} (4 x^{3}) = 0

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

Vereinfache

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

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