(\partial)/(\partial x)(2x^2+y^2+2xy+yx+7y)

Lösung

\frac{\partial}{\partial x} (2 x^{2} + y^{2} + 2 x y + y x + 7 y)

4 x + 3 y

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x^{2} + y^{2} + 2 x y + y x + 7 y)

Vereinfache

2 x^{2} + y^{2} + 2 x y + y x + 7 y : 2 x^{2} + y^{2} + 3 x y + 7 y

= \frac{\partial}{\partial x} (2 x^{2} + y^{2} + 3 x y + 7 y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (2 x^{2}) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (3 x y) + \frac{\partial}{\partial x} (7 y)

\frac{\partial}{\partial x} (2 x^{2}) = 4 x

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

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

\frac{\partial}{\partial x} (7 y) = 0

= 4 x + 0 + 3 y + 0

Vereinfache

= 4 x + 3 y

\frac{\partial}{\partial v} (ln (u cos (v)))

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

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

x \to \infty lim (- 1)

a re a 2 x^{2}, x^{4} - 2 x^{2}