Step-by-step explanation:
[tex]y = 6u {}^{3} + 5u + 2[/tex]
[tex]y = 6( - 3 {x}^{2} - 4x + 9) {}^{3} + 5( - 3 {x}^{2} - 4x + 9) + 2[/tex]
Use the chain rule.
[tex] \frac{dy}{dx} = 6(3)( - 3 {x}^{2} - 4x + 9) {}^{2} ( - 6x - 4) + 5( - 6x - 4)[/tex]
[tex]18( - 3 {x}^{2} - 4x + 9) {}^{2} ( - 6x - 4) + 5( - 6x - 4)[/tex]
Factor out -6x-4,
[tex]( - 6x - 4)(18( - 3 {x}^{2} - 4x + 9) {}^{2} + 5)[/tex]
Know plug in x=-2 to evaluate the derivative
[tex]( - 6(2) - 4)(18( - 3(2) {}^{2} - 4(2) + 9) {}^{2} + 5)[/tex]
[tex]( - 16)(18(( - 12) - 8 + 9)) {}^{2} + 5)[/tex]
[tex] - 16(18( - 11) {}^{2} + 5)[/tex]
[tex] - 16(2183)[/tex]
[tex] - 34928[/tex]
