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Beliebt Rechnen >

derivative of ye^{xy}

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

Beliebte Beispiele

integral from 0 to 2 of 1/(sqrt(2-x))

\int_{0}^{2} \frac{1}{2 - x} d x

integral of (sin(x))^{-1}

\int (sin (x))^{- 1} d x

fläche-x,x-x^2,0,2

a re a - x, x - x^{2}, 0, 2

integral of (x^3)/1+x^4

\int \frac{x ^{3}}{1} + x^{4} d x

integral of cos(n*x)

\int cos (n \cdot x) d x