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

Lösung

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

- 2 y^{2} z x + 2 y^{2} z^{2}

Schritte zur Lösung

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

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

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

= - 2 y^{2} z x + 2 y^{2} z^{2}

\frac{d}{d x} ((x + y)^{\frac{1}{2}})

\int 5 x arctan (x) d x

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

\frac{d}{d x} (ln ((x - 1)^{3} (x^{2} + 1)^{4}))

\frac{d}{d x} (3 x^{2} - e^{2 x})