(\partial)/(\partial x)(x^2y-2xy+yz^2)

Lösung

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

2 x y - 2 y

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= 2 y x - 2 y + 0

Vereinfache

= 2 x y - 2 y

s l o p e (- 2, 3), (4, - 5)

n = 0 \sum \infty \frac{e ^{n}}{n !}

\frac{\partial}{\partial x} (10 x e^{- x^{2} - y^{2}})

d er i v a t i v e θ cos (θ) sin (θ)

x^{2} \frac{d y}{d x} - y^{3} = x y