(\partial)/(\partial x)((z)(x^2+y^2-z^2))

Lösung

\frac{\partial}{\partial x} ((z) (x^{2} + y^{2} - z^{2}))

2 z x

Schritte zur Lösung

\frac{\partial}{\partial x} ((z) (x^{2} + y^{2} - z^{2}))

Behandle

z, y

als Konstanten

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= z (2 x + 0 - 0)

Vereinfache

= 2 z x

e x p an d 4^{3}

s im pl i f y x^{2} - 2 (a + \frac{1}{a}) x + 4

s im pl i f y \frac{9 ( x - 2 ) ^{2}}{4}

e x p an d \frac{34 ( s + 4 )}{( s ^{2} + 2 s + 2 ) ( s ^{2} + 16 s + 68 )}

e x p an d (sin (x + y) - cos (x) sin (y)) \cdot sec (y)