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

Lösung

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

2 x

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= 2 x + 0 - 0

Vereinfache

= 2 x

\int 3 - \frac{1}{3} \cdot (x - 4)^{2} d x

\int_{0}^{2} \frac{x ^{2} - 2}{x + 1} d x

y^{^{'}} = \frac{x ^{2} y + y ^{3}}{x ^{3}}

x \to 0 lim (3 + x^{2} sin (\frac{1}{x}))

s l o p e y = \frac{1}{x - 4}, x = 8