Determine \( y^{\prime \prime} \), sabiendo que \( y=f(x) \) es una curva definida implícitamente por la ecuación: \[ \begin{array}{c}x^{3}-9+y^{3}=x y\end{array} \]

1) si \( \left(x^{2}+y^{2}\right)^{2}+3 x y-y^{2}=0 \quad \) halle \( \frac{d y}{d x} \left\lvert\,\left(\frac{1}{2},-\frac{1}{2}\right)\right. \)

1) \( y=3 x^{3}-6 x^{3}+11 x-8 x^{2} \) 2) \( y=-4 x^{-\frac{2}{3}}-8 x^{-\frac{3}{4}}+4 x^{-3}+5 x \) 3) \( y=6 x^{-\frac{1}{2}}+8 x^{-\frac{3}{4}}-6 x^{-1}-4 x^{-3} \)

\( x^{3}-x-4=0 \) in the interval. (1,2) in 10 iterations.

1) \( y=3 x^{3}-6 x^{\frac{5}{3}}+11 x-8 x^{\frac{3}{2}} \) 2

implications. 10. Deseribe how vector calculas is utilized in electromagnetiom, specif- eally in calculating electric flelds.