(\partial)/(\partial x)((4x+4y)e^y)

Lösung

\frac{\partial}{\partial x} ((4 x + 4 y) e^{y})

4 e^{y}

Schritte zur Lösung

\frac{\partial}{\partial x} ((4 x + 4 y) e^{y})

Behandle

y

als Konstante

Entferne die Konstante:

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

= e^{y} \frac{\partial}{\partial x} (4 x + 4 y)

Wende die Summen-/Differenzregel an:

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

= e^{y} (\frac{\partial}{\partial x} (4 x) + \frac{\partial}{\partial x} (4 y))

\frac{\partial}{\partial x} (4 x) = 4

\frac{\partial}{\partial x} (4 y) = 0

= e^{y} (4 + 0)

Vereinfache

= 4 e^{y}

l a pl a ce t r an s f or m 2 e^{- t} cos (2 t)

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\int \frac{6 x ^{3} + 3 x ^{2} - 47 x - 18}{x ^{2} - 9} d x