(\partial)/(\partial x)(xy+yz+zx)

Lösung

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

y + z

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial x} (yz) = 0

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

= y + 0 + z

Vereinfache

= y + z

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

4 y^{^{''}} - 12 y^{^{'}} + 9 y = 0, y (0) = 3, y^{^{'}} (0) = 5

n \to \infty lim (\frac{ln ( n )}{ln ( 2 n )})

\int \frac{1}{( x - 3 ) ( x + 4 )} d x

x \to 0 lim (x^{0})