d/(dy)((x)(xe^{y/x}+ye^{x/y}))

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

e x p an d a^{2} + 6 a + 9 - (a + 4) (a + 2)^{'}

e x p an d (5 x + 3) d e

\frac{d}{d t} ((s) (\frac{3}{4 π} cos (4 t) + \frac{3}{7 π} sin (7 t)))

e x p an d \frac{1}{2 ( x + 7 )}

e x p an d - 5 (\frac{- 5 - 3 y}{10} - 4 y = 10)