(\partial)/(\partial x)(2xyz+xy^2+xz)

Lösung

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

2 yz + y^{2} + z

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= 2 yz + y^{2} + z

d er i v a t i v e \frac{4 x}{x + 2}

x \to o lim (\frac{cos ( x )}{x})

\frac{d}{d x} (arccos (\frac{1 - x}{1 + x}))

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

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