(\partial)/(\partial x)(x^2-xy+y^2+3x-2y+1)

Lösung

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

2 x + 3 - y

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial x} (x y) = y

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

\frac{\partial}{\partial x} (3 x) = 3

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

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

= 2 x - y + 0 + 3 - 0 + 0

Vereinfache

= 2 x + 3 - y

y^{2} = 2 x y y^{^{'}}

x \to - 1 lim (2)

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

y^{^{'}} + \frac{3}{x} y = \frac{1}{x ^{2}}

\frac{d}{d x} (4 - 3 sin (3 x))