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Beliebt Rechnen >

derivative of xe^{y^2}

Lösung

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

Lösung

e^{y^{2}} + 2 e^{y^{2}} x y \frac{d y}{d x}

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{y^{2}}

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

\frac{d x}{d x} = 1

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

= 1 \cdot e^{y^{2}} + e^{y^{2}} \cdot 2 y \frac{d y}{d x} x

Vereinfache

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

Beliebte Beispiele

derivative of (-x^2/2)

\frac{d}{d x} (\frac{- x ^{2}}{2})

limit as x approaches c/(2^+) of [2x-4]

x \to \frac{c}{2 ^{+}} lim ([2 x - 4])

y^{^{''}} + y = 3

integral of (sin(t))

\int (sin (t)) d t

derivative-2x^3

d er i v a t i v e - 2 x^{3}