Pregunta: Differentiate. a) y=x3−12x2+x−1 b) y=(x+2x)ex

Differentiate using the Quotient Rule which states that $\frac{\mathrm{d}}{\mathrm{d}\mathrm{x}}\left[\frac{\mathrm{f}\left(\mathrm{x}\right)}{\mathrm{g}\left(\mathrm{x}\right)}\right]$ is $\frac{\mathrm{g}\left(\mathrm{x}\right)\frac{\mathrm{d}}{\mathrm{d}\mathrm{x}}\left[\mathrm{f}\left(\mathrm{x}\right)\right]-\mathrm{f}\left(\mathrm{x}\right)\frac{\mathrm{d}}{\mathrm{d}\mathrm{x}}\left[\mathrm{g}\left(\mathrm{x}\right)\right]}{{\mathrm{g}\left(\mathrm{x}\right)}^2}$ where $\mathrm{f}\left(\mathrm{x}\right)=2{\mathrm{x}}^2+\mathrm{x}-1$ and $\mathrm{g}\left(\mathrm{x}\right)={\mathrm{x}}^3-1$ .

$\frac{({\mathrm{x}}^3-1)\frac{\mathrm{d}}{\mathrm{d}\mathrm{x}}[2{\mathrm{x}}^2+\mathrm{x}-1]-(2{\mathrm{x}}^2+\mathrm{x}-1)\frac{\mathrm{d}}{\mathrm{d}\mathrm{x}}[{\mathrm{x}}^3-1]}{{({\mathrm{x}}^3-1)}^2}$