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

Lösung

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

4 x^{3} - 2 x y

Schritte zur Lösung

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

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

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

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

\frac{\partial}{\partial x} (2 y^{3}) = 0

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

Vereinfache

= 4 x^{3} - 2 x y

\frac{d y}{d x} = 3 y + 4

\int cos^{4} (7 x + 2) d x

t an g e n t y = 6 e^{x} + x, (0, 6)

\frac{\partial}{\partial x} (e^{z} + \frac{1}{x} + x e^{- y})

\frac{d y}{d x} = \frac{4 y ln ( x )}{x}, y (e) = 1