(\partial)/(\partial x)(7-x^4+2x^2-y^2)

Lösung

\frac{\partial}{\partial x} (7 - x^{4} + 2 x^{2} - y^{2})

- 4 x^{3} + 4 x

Schritte zur Lösung

\frac{\partial}{\partial x} (7 - 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} (7) - \frac{\partial}{\partial x} (x^{4}) + \frac{\partial}{\partial x} (2 x^{2}) - \frac{\partial}{\partial x} (y^{2})

\frac{\partial}{\partial x} (7) = 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 y}{d x} + 5 y = e^{x} y^{- 2}

\frac{d}{d x} ((x^{2} - 2) sin (x) + 2 x cos (x))

x \to 2 lim (\frac{∣ x - 3 ∣}{x - 3})

\int tan^{3} (5 x) sec^{2} (5 x) d x

\frac{d}{d x} (\frac{1 + cos ( x )}{1 - cos ( x )})