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

Lösung

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

e^{x - y}

Schritte zur Lösung

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

Behandle

x, y

als Konstanten

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial z} (x) = 0

\frac{\partial}{\partial z} (z) = 1

= e^{x - y} (0 + 1)

Vereinfache

= e^{x - y}

\int \frac{1}{9 e ^{- 2 x} + e ^{2 x}} d x

y^{^{'}} + x^{- 1} y = \frac{2}{3} x^{4} y^{4}

\frac{\partial}{\partial x} (x e^{x} + e^{x})

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

y^{^{''}} - 14 y^{^{'}} + 50 y = 0, y (0) = 10, y (\frac{π}{2}) = 3