(\partial)/(\partial z)(x^2yz+1/(xyz^2))

Lösung

\frac{\partial}{\partial z} (x^{2} yz + \frac{1}{x y z ^{2}})

x^{2} y - \frac{2}{x y z ^{3}}

Schritte zur Lösung

\frac{\partial}{\partial z} (x^{2} yz + \frac{1}{x y z ^{2}})

Behandle

x, y

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial z} (x^{2} yz) + \frac{\partial}{\partial z} (\frac{1}{x y z ^{2}})

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

\frac{\partial}{\partial z} (\frac{1}{x y z ^{2}}) = - \frac{2}{x y z ^{3}}

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

\int \frac{1}{25 x ^{2} + 2} d x

2 x y y^{^{'}} = 3 y^{2} + x^{2}

x \to 1 + lim (3 x - 1)

\int \frac{1}{x ^{3} - 1} d x

im pl i c i t \frac{d y}{d x}, x^{2} - y^{3} = 6