Use product Rule to find \( f^{\prime}(x) \) where \( f(x)=(x+2)\left(3 x^{3}-5 x\right) \) Type your answer starting with the term with highest degree \( \square \)

To find the derivative \( f^{\prime}(x) \) using the product rule, we first set \( u = x + 2 \) and \( v = 3x^3 - 5x \). The product rule states: \[ f^{\prime}(x) = u'v + uv' \] Calculating \( u' \) and \( v' \): \[ u' = 1, \quad v' = 9x^2 - 5 \] Now, applying the product rule: \[ f^{\prime}(x) = (1)(3x^3 - 5x) + (x + 2)(9x^2 - 5) \] Simplifying: \[ f^{\prime}(x) = 3x^3 - 5x + (x + 2)(9x^2 - 5) \] Now, multiply out \( (x + 2)(9x^2 - 5) \): \[ = 9x^3 - 5x + 18x^2 - 10 \] Combine everything: \[ = 3x^3 - 5x + 9x^3 + 18x^2 - 10 - 5x \] \[ = (3x^3 + 9x^3) + 18x^2 + (-5x - 5x) - 10 \] \[ = 12x^3 + 18x^2 - 10 \] So the final answer is: \[ f^{\prime}(x) = 12x^3 + 18x^2 - 10 \]