(\partial)/(\partial y)(({f}(y,x))(2x+2y))

Lösung

\frac{\partial}{\partial y} ((f (y, x)) (2 x + 2 y))

\frac{\partial}{\partial y} (f (y, x)) (2 x + 2 y) + 2 f (y, x)

Schritte zur Lösung

\frac{\partial}{\partial y} ((f (y, x)) (2 x + 2 y))

Behandle

x

als Konstante

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = f (y, x), g = 2 x + 2 y

= \frac{\partial}{\partial y} (f (y, x)) (2 x + 2 y) + \frac{\partial}{\partial y} (2 x + 2 y) f (y, x)

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

= \frac{\partial}{\partial y} (f (y, x)) (2 x + 2 y) + 2 f (y, x)

e x p an d A (6, - 2)

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

e x p an d (-) (x + 1) (- x + 3)

e x p an d \frac{p ( s - 2 )}{2}

e x p an d \frac{5 ( 4 x ^{5} + 1 ) ( x + x ^{5} - 1 ) ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}