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Beliebt Rechnen >

(\partial)/(\partial x)(6x^2+3y^2+xy)

Lösung

\frac{\partial}{\partial x} (6 x^{2} + 3 y^{2} + x y)

Lösung

12 x + y

Schritte zur Lösung

\frac{\partial}{\partial x} (6 x^{2} + 3 y^{2} + x y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (6 x^{2}) + \frac{\partial}{\partial x} (3 y^{2}) + \frac{\partial}{\partial x} (x y)

\frac{\partial}{\partial x} (6 x^{2}) = 12 x

\frac{\partial}{\partial x} (3 y^{2}) = 0

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

= 12 x + 0 + y

Vereinfache

= 12 x + y

Beliebte Beispiele

steigung sqrt(7x+1)(9.8)

s l o p e 7 x + 1 (9.8)

f^{^{'}} (x) = e^{x^{2}}

integral of 1/(3x+4)

\int \frac{1}{3 x + 4} d x

limit as x approaches 0 of 2/(x^3)

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

x^2(dy)/(dx)+y^2-xy=0

x^{2} \frac{d y}{d x} + y^{2} - x y = 0