derivative of xe^xy

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

\frac{d ^{3}}{d x ^{3}} (cos (x) - sin (x))

\int \frac{6}{x ( x + 2 )} d x

x \to 3 + lim (\frac{∣ x - 2 ∣}{x - 2})

\frac{\partial}{\partial x} (56 x^{2} - 8 y^{2} - 16 x - 31 + 1 - 8 x)

f (x) = 1 + x