(\partial)/(\partial z)((x)(x+2z))

Lösung

\frac{\partial}{\partial z} ((x) (x + 2 z))

2 x

Schritte zur Lösung

\frac{\partial}{\partial z} ((x) (x + 2 z))

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= x (0 + 2)

Vereinfache

= 2 x

e x p an d \frac{n !}{( n ( n - 1 ) ) !}

e x p an d (x + 3 y - 2 z)^{5}

e x p an d \frac{e ^{- 2 s}}{( s ^{2} + 1 ) ( s ^{2} + 9 )}

e x p an d \frac{s ^{2} + s + 16}{( s ^{2} + 16 ) ^{2}}

e x p an d e^{x^{6} e^{x}} \cdot (x - 4 y = x^{6} e^{x})