Find $y^{\text{'}}$ by $($a$)$ applying the Product Rule and $($b$)$ multiplying the factors to produce a sum of simpler terms to differentiate

$y=(6-x^2)(x^3-5x+3)$

a$.$ Apply the Product Rule. Let $u=(6-x^2)$ and $v=(x^3-5x+3)$

$\frac{d}{dx}(uv)=(6-x^2)|,|+(x^3-5x+3)$

b$.$ Multiply the factors of the original expression, $u$ and $v,$ to produce a sum of simpler terms.

$y=$

$($Simplify your answer.$)$

Find $y^{\text{'}}.$

$y^{\text{'}}=$