Question

Use the product rule to find the derivative of the following. (Hint: Write the quantity as a product.)k(t) = (t² − 2) ²k' (t) =

Answer 1

`\begin{gathered} The\text{ product Rule is used to calculate:} \\ (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} \\ (d)/(dx)(t^2-2)(t^2-2) \\ \end{gathered}`
`\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}`