(\partial)/(\partial x)(2-x^4+2x^2-y^2)

Lösung

\frac{\partial}{\partial x} (2 - x^{4} + 2 x^{2} - y^{2})

- 4 x^{3} + 4 x

Schritte zur Lösung

\frac{\partial}{\partial x} (2 - x^{4} + 2 x^{2} - y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (2) - \frac{\partial}{\partial x} (x^{4}) + \frac{\partial}{\partial x} (2 x^{2}) - \frac{\partial}{\partial x} (y^{2})

\frac{\partial}{\partial x} (2) = 0

\frac{\partial}{\partial x} (x^{4}) = 4 x^{3}

\frac{\partial}{\partial x} (2 x^{2}) = 4 x

\frac{\partial}{\partial x} (y^{2}) = 0

= 0 - 4 x^{3} + 4 x - 0

Vereinfache

= - 4 x^{3} + 4 x

\frac{d}{d x} (\frac{( e ^{x} )}{1 + x})

\frac{\partial}{\partial x} (- 10 e^{- 5 x^{2} - y^{2}} x)

\frac{d}{d x} (\frac{2}{3 3 x})

\int - 0.2 t^{2} + 3 d t

\frac{\partial}{\partial x} (sin (π \cdot x))