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

Lösung

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

- \frac{e ^{\frac{y}{x}} y}{x ^{2}}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial y} (\frac{e ^{\frac{y}{x}} y}{x}) = \frac{e ^{\frac{y}{x}} y + x e ^{\frac{y}{x}}}{x ^{2}}

= \frac{e ^{\frac{y}{x}}}{x} - \frac{e ^{\frac{y}{x}} y + x e ^{\frac{y}{x}}}{x ^{2}}

Vereinfache

\frac{e ^{\frac{y}{x}}}{x} - \frac{e ^{\frac{y}{x}} y + x e ^{\frac{y}{x}}}{x ^{2}} : - \frac{e ^{\frac{y}{x}} y}{x ^{2}}

= - \frac{e ^{\frac{y}{x}} y}{x ^{2}}

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

so l v e f or x, \frac{d ^{2} x}{d t ^{2}} + x = (t^{2} + t) sin (t)

s l o p e (- 5, 11), (- 10, 6)

\int \frac{ln ( 2 x )}{x ^{2}} d x

y^{\frac{1}{2}} (\frac{d y}{d x}) + y^{\frac{3}{2}} = 1, y (0) = 9