(\partial)/(\partial y)(x^2+2y^2+3xz)

Lösung

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

4 y

Schritte zur Lösung

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

Behandle

x, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{\partial}{\partial y} (3 x z) = 0

= 0 + 4 y + 0

Vereinfache

= 4 y

x \to - 2 lim (\frac{1}{x + 1})

\int \frac{4}{x ln ( 5 x )} d x

\int \frac{1}{( 441 + x ^{2} ) ^{\frac{3}{2}}} d x

x^{^{'}} = k (300 - x)

\frac{d}{d x} (\frac{8 x ^{3} - 9}{x ^{2}})