d/(d{x)}(({z})({x}^2+{y}^2+{z}^2))

Lösung

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

2 z x

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= z (2 x + 0 + 0)

Vereinfache

= 2 z x

e x p an d \frac{5 ( 4 - 3 x ^{2} )}{( 4 + 3 x ^{2} ) ^{2}}

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e x p an d P_{1} (6, 1) P_{2} (1, - 4)

e x p an d \frac{1}{s ( s + 1 ) ^{3}}

s im pl i f y (x + 2 + 2 i) \cdot (x + 2 i) \cdot (x - 1 + i)