d/(d{x)}(({z})({x}^2+2{y}^2+3{z}^2-1))

Lösung

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

2 z x

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{d}{d x} (3 z^{2}) = 0

\frac{d}{d x} (1) = 0

= z (2 x + 0 + 0 - 0)

Vereinfache

= 2 z x

e x p an d (3 + x) x^{2} e^{7 x}

e x p an d x^{\frac{2}{5}} (y^{\frac{1}{2}} + 2 x^{\frac{6}{5}})^{6}

e x p an d \frac{( x ^{2} + x - 125 ) ( x - 5 )}{( x + 4 ) ( x ^{2} - 9 )}

e x p an d - \frac{d}{d x} (\frac{x - a}{( x - a ) ^{2} + b ^{2}})

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