(\partial)/(\partial x)((2x+5y)e^y)

Lösung

\frac{\partial}{\partial x} ((2 x + 5 y) e^{y})

2 e^{y}

Schritte zur Lösung

\frac{\partial}{\partial x} ((2 x + 5 y) e^{y})

Behandle

y

als Konstante

Entferne die Konstante:

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

= e^{y} \frac{\partial}{\partial x} (2 x + 5 y)

Wende die Summen-/Differenzregel an:

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

= e^{y} (\frac{\partial}{\partial x} (2 x) + \frac{\partial}{\partial x} (5 y))

\frac{\partial}{\partial x} (2 x) = 2

\frac{\partial}{\partial x} (5 y) = 0

= e^{y} (2 + 0)

Vereinfache

= 2 e^{y}

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

\int_{0}^{8} (x + 1)^{2} d x

x \to 0 lim (\frac{ln ( 1 - 6 x )}{x})

x \to - 8 lim (\frac{∣ x + 8 ∣}{x + 8})

d er i v a t i v e - \frac{4 x}{y}