(\partial)/(\partial z)(6ze^{xyz})

Lösung

\frac{\partial}{\partial z} (6 z e^{x yz})

6 (e^{z x y} + e^{z x y} z x y)

Schritte zur Lösung

\frac{\partial}{\partial z} (6 z e^{x yz})

Behandle

x, y

als Konstanten

Entferne die Konstante:

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

= 6 \frac{\partial}{\partial z} (z e^{x yz})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = z, g = e^{x yz}

= 6 (\frac{\partial}{\partial z} (z) e^{x yz} + \frac{\partial}{\partial z} (e^{x yz}) z)

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

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

= 6 (1 \cdot e^{x yz} + e^{x yz} x yz)

Vereinfache

= 6 (e^{z x y} + e^{z x y} z x y)

\int - x^{2} + 4 x + 5 d x

d er i v a t i v e f (x) = - 8 x

\frac{d}{d x} (\frac{arccos ( x )}{( x + 1 ) ^{2}})

\frac{d}{d x} (e^{g (x)} sin (x))

\int_{- \infty}^{12} x e^{\frac{x}{4}} d x