d/(d{x)}({x}^2+2{y}^2+{z}^2-6{x}+3{y}-2{z}+5)

Lösung

\frac{d}{d x} (x^{2} + 2 y^{2} + z^{2} - 6 x + 3 y - 2 z + 5)

2 x - 6

Schritte zur Lösung

\frac{d}{d x} (x^{2} + 2 y^{2} + z^{2} - 6 x + 3 y - 2 z + 5)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{2}) + \frac{d}{d x} (2 y^{2}) + \frac{d}{d x} (z^{2}) - \frac{d}{d x} (6 x) + \frac{d}{d x} (3 y) - \frac{d}{d x} (2 z) + \frac{d}{d x} (5)

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

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

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

\frac{d}{d x} (6 x) = 6

\frac{d}{d x} (3 y) = 0

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

\frac{d}{d x} (5) = 0

= 2 x + 0 + 0 - 6 + 0 - 0 + 0

Vereinfache

= 2 x - 6

y^{^{''}} - 6 y^{^{'}} + 0 y = 0

\int \frac{5}{e ^{x} + 2} d x

\frac{d y}{d x} + 3 x y^{3} = 0

\int \frac{5 t - 4}{t + 1} d t

x \to - 1 lim (0)