(\partial)/(\partial x)(3x^2+4xy+2y^2)

Lösung

\frac{\partial}{\partial x} (3 x^{2} + 4 x y + 2 y^{2})

6 x + 4 y

Schritte zur Lösung

\frac{\partial}{\partial x} (3 x^{2} + 4 x y + 2 y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (3 x^{2}) + \frac{\partial}{\partial x} (4 x y) + \frac{\partial}{\partial x} (2 y^{2})

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

\frac{\partial}{\partial x} (4 x y) = 4 y

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

= 6 x + 4 y + 0

Vereinfache

= 6 x + 4 y

t an g e n t 4 cos (x), at x = - \frac{π}{3}

a re a (x^{2} - 12), (x - 6)

\frac{d}{d x} (x^{3} - x - 1)

d er i v a t i v e (x - 2)^{2} - sin (3 x)

\int \frac{3 - 2 x}{5 x + 7} d x