(\partial)/(\partial x)(x^7yz^2+7yz)

Lösung

\frac{\partial}{\partial x} (x^{7} y z^{2} + 7 yz)

7 x^{6} y z^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{7} y z^{2} + 7 yz)

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{7} y z^{2}) + \frac{\partial}{\partial x} (7 yz)

\frac{\partial}{\partial x} (x^{7} y z^{2}) = 7 y z^{2} x^{6}

\frac{\partial}{\partial x} (7 yz) = 0

= 7 y z^{2} x^{6} + 0

Vereinfache

= 7 x^{6} y z^{2}

a re a x = y, x = - y^{2} + 6 y

\int_{50}^{80} \frac{25}{3} x d x

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\frac{\partial}{\partial x} (e^{- 3 x - y})