Find \( \frac{d^{2} y}{d x^{2}} \) given \( x^{3}-3 x y+y^{3}=1 \)

Determine the first derivative of the \( 1.1 \quad y=x^{3}-\cot \left(x^{3}+3 x-1\right) \)

Calcula el área entre las curvas \( y = x^3 - 3x \) y \( y = x + 1 \) sobre el intervalo definido por sus intersecciones.

кцияның туындысын табыңыз: \( \left\{\begin{array}{l}x=t^{3}+3 t^{2}-5 \\ y=3 t^{2}+6 t-3\end{array}\right. \)

A solid is formed with triangular cross-sections where each triangle's base is defined by the equation \(y = x^2\) on interval \([0, 2]\). What is the volume of this solid?

\( \int _{0}^{\frac{\pi }{2}}\frac{1}{2+\cos (x)} d x \)