(\partial)/(\partial y)(xy+yz+zy)

Lösung

\frac{\partial}{\partial y} (x y + yz + zy)

x + 2 z

Schritte zur Lösung

\frac{\partial}{\partial y} (x y + yz + zy)

Vereinfache

x y + yz + zy : x y + 2 yz

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

Behandle

x, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial y} (2 yz) = 2 z

= x + 2 z

d er i v a t i v e f (x) = - \frac{1}{9} (x^{- 9} - x^{18})

\int \frac{1}{16 e ^{- 5 x} + e ^{5 x}} d x

t an g e n t (4 - x) y^{2} = x^{3}, (2, 2)

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

\int 4 x^{7} d x