(\partial)/(\partial x)((z)(e^{2z}-xyz))

Lösung

\frac{\partial}{\partial x} ((z) (e^{2 z} - x yz))

- z^{2} y

Schritte zur Lösung

\frac{\partial}{\partial x} ((z) (e^{2 z} - x yz))

Behandle

z, y

als Konstanten

Entferne die Konstante:

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

= z \frac{\partial}{\partial x} (e^{2 z} - x yz)

Wende die Summen-/Differenzregel an:

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

= z (\frac{\partial}{\partial x} (e^{2 z}) - \frac{\partial}{\partial x} (x yz))

\frac{\partial}{\partial x} (e^{2 z}) = 0

\frac{\partial}{\partial x} (x yz) = zy

= z (0 - zy)

Vereinfache

z (0 - zy) : - z^{2} y

= - z^{2} y

e x p an d \frac{3 ( x - 1 )}{4}

e x p an d (ln (1 + \frac{1}{x}) - \frac{1}{x + 1}) (1 + \frac{1}{x})^{x}

\frac{d ^{2}}{d x ^{2}} ((y) ((3 x^{2} - 1)^{2}))

e x p an d \frac{( 0.675 + 2 x ) ^{2}}{( 0.5643 - x ) ( 0.7653 - x )}

s im pl i f y (x - 2) (x - 3) (x - 5) (x + 5)