d/(dy)(1+ye^{xy})

Lösung

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

e^{y x} + e^{y x} y x

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d y} (1) = 0

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

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

Vereinfache

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

\int x tan (π x) d x

\frac{\partial}{\partial x} (sin (4 x - 2 y))

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

\frac{\partial}{\partial x} (x e^{- 3 x y})

n = 1 \sum \infty \frac{n}{3}