(\partial)/(\partial x)(x^2+10xy+y^2)

Lösung

\frac{\partial}{\partial x} (x^{2} + 10 x y + y^{2})

2 x + 10 y

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} + 10 x y + y^{2})

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

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

\frac{\partial}{\partial x} (10 x y) = 10 y

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

= 2 x + 10 y + 0

Vereinfache

= 2 x + 10 y

x \to 0 + lim (x \cdot (e^{\frac{1}{x}} - 1))

\int (\frac{1}{x} + \frac{x x}{3}) d x

\frac{d}{d x} (arctan (x))

\frac{d}{d x} (lo g_{5} (2 x^{2}))

\frac{d}{d y} (e^{y} cos (y))