(\partial)/(\partial y)(x^2-5xy+3y^2)

Lösung

\frac{\partial}{\partial y} (x^{2} - 5 x y + 3 y^{2})

6 y - 5 x

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{2} - 5 x y + 3 y^{2})

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (x^{2}) - \frac{\partial}{\partial y} (5 x y) + \frac{\partial}{\partial y} (3 y^{2})

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

\frac{\partial}{\partial y} (5 x y) = 5 x

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

= 0 - 5 x + 6 y

Vereinfache

= 6 y - 5 x

\int 4 x^{2} - 16 x + 16 d x

x \to 1 lim (\frac{x ^{4} - 1}{x - 1})

t an g e n t f (- 2) = 2 x^{4}

\frac{d}{d x} ((4 x + 1)^{2})

\frac{d}{d x} (\frac{1}{( 1 - 2 x )})