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Beliebt Rechnen >

derivative ay(e^{by})

Lösung

ableitung von

a y (e^{b y})

Lösung

a (e^{b y} + b e^{b y} y)

Schritte zur Lösung

\frac{d}{d y} (a y e^{b y})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= a \frac{d}{d y} (y e^{b y})

Wende die Produktregel an:

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

f = y, g = e^{b y}

= a (\frac{d y}{d y} e^{b y} + \frac{d}{d y} (e^{b y}) y)

\frac{d y}{d y} = 1

\frac{d}{d y} (e^{b y}) = e^{b y} b

= a (1 \cdot e^{b y} + e^{b y} b y)

Vereinfache

= a (e^{b y} + b e^{b y} y)

Beliebte Beispiele

derivative ln(-x)

d er i v a t i v e ln (- x)

integral of (12)/(x^{-1)+3}

\int \frac{12}{x ^{- 1} + 3} d x

derivative of 1/(2x+9)

\frac{d}{d x} (\frac{1}{2 x + 9})

integral from 1 to 4 of (2x+1)

\int_{1}^{4} (2 x + 1) d x

limit as x approaches-2 of sqrt(8+x^2)

x \to - 2 lim (8 + x^{2})