(\partial)/(\partial z)(yz^2-ln(x+z))

Lösung

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

2 yz - \frac{1}{x + z}

Schritte zur Lösung

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

Behandle

y, x

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial z} (ln (x + z)) = \frac{1}{x + z}

= 2 yz - \frac{1}{x + z}

f a c t or 3 x^{6} - 6 x^{6} y^{7} + 4 x^{5} y^{4}

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d er i v a t i v e f (x) = (x + \frac{1}{3 x})^{2}