[tex]\begin{gathered} The\text{ product Rule is used to calculate:} \\ \frac{d}{dx}(f(x)*g(x)) \\ =\text{ f'\lparen x\rparen *g\lparen x\rparen + f\lparen x\rparen *g'\lparen x\rparen} \\ In\text{ our case f\lparen x\rparen = g\lparen x\rparen. We therefore need to find} \\ \frac{d}{dx}(t^2-2)(t^2-2) \\ \end{gathered}[/tex][tex]\begin{gathered} f^{\prime}(x)\text{ = g'\lparen x\rparen} \\ =2t \\ Therefore \\ f^{\prime}(x)*g(x)\text{ + f\lparen x\rparen *g'\lparen x\rparen} \\ =\text{ 2t\lparen t}^2-2)\text{ + 2t\lparen t}^2-2) \\ =\text{ 4t\lparen t}^2-2) \end{gathered}[/tex]
