(\partial)/(\partial x)(x^3y-xy^3)

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

t an g e n t f (x) = \frac{4}{x}, at x = 3

x \to 0 lim (x^{2} cos (\frac{2}{x}))

n = 1 \sum \infty \frac{1}{3 ^{n} + n}

\frac{d y}{d x} = y (3 y - 6)

x \to 0 + lim (\frac{tan ( x )}{x})