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

Lösung

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

x^{2} + 2 yz

Schritte zur Lösung

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

Behandle

x, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial y} (y^{2} z) = 2 zy

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

= x^{2} + 2 zy + 0

Vereinfache

= x^{2} + 2 yz

d er i v a t i v e f (x) = \frac{6 x - 1}{x ^{3}}

\int_{3}^{5} x^{3} d x

\int_{0}^{3} \frac{1}{x - 2} d x

a re a x, 2 x 81 - x^{2}

\int 1 + cos^{2} (x) d x