derivative of 6(x^3-3(x)(y)+3(y)^3)

Lösung

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

18 x^{2} - 3 (y + x \frac{d y}{d x}) + 9 y^{2} \frac{d y}{d x}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (6 x^{3}) = 18 x^{2}

\frac{d}{d x} (3 x y) = 3 (y + x \frac{d y}{d x})

\frac{d}{d x} (3 y^{3}) = 9 y^{2} \frac{d y}{d x}

= 18 x^{2} - 3 (y + x \frac{d y}{d x}) + 9 y^{2} \frac{d y}{d x}

\int_{0}^{5} \frac{6}{7 x ^{2} + 8 x + 1} d x

\int x^{2} (4 x^{3} + 2)^{3} d x

t an g e n t y = x^{2}, (- 1, - 3)

\int_{v^{1}}^{v^{2}} \frac{1}{v} d v

x \to - 1 lim (\frac{1}{x ^{2} - 1})