(\partial)/(\partial x)(x^4-3x^2y^2+y^4)

Lösung

\frac{\partial}{\partial x} (x^{4} - 3 x^{2} y^{2} + y^{4})

4 x^{3} - 6 x y^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{4} - 3 x^{2} y^{2} + y^{4})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{4}) - \frac{\partial}{\partial x} (3 x^{2} y^{2}) + \frac{\partial}{\partial x} (y^{4})

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

\frac{\partial}{\partial x} (3 x^{2} y^{2}) = 6 y^{2} x

\frac{\partial}{\partial x} (y^{4}) = 0

= 4 x^{3} - 6 y^{2} x + 0

Vereinfache

= 4 x^{3} - 6 x y^{2}

y^{^{''}} - y^{^{'}} - 2 y = 0, y (0) = 0, y (\frac{π}{2}) = 1

d er i v a t i v e f (x) = 4 x^{2} - 1

t an g e n t y = (1 + 5 x)^{12}, (0, 1)

\frac{d x}{d t} = sin (x)

\int x^{2} (x - 7) d x