Question

Evaluate dydx at x=2 for the function below.

y=6u^3+5u+2, where u=−3x^2−4x+9

Answer 1

Explanation:

`y = 6u {}^(3) + 5u + 2`

`y = 6( - 3 {x}^(2) - 4x + 9) {}^(3) + 5( - 3 {x}^(2) - 4x + 9) + 2`

Use the chain rule.

`(dy)/(dx) = 6(3)( - 3 {x}^(2) - 4x + 9) {}^(2) ( - 6x - 4) + 5( - 6x - 4)`

`18( - 3 {x}^(2) - 4x + 9) {}^(2) ( - 6x - 4) + 5( - 6x - 4)`

Factor out -6x-4,

`( - 6x - 4)(18( - 3 {x}^(2) - 4x + 9) {}^(2) + 5)`

Know plug in x=-2 to evaluate the derivative

`( - 6(2) - 4)(18( - 3(2) {}^(2) - 4(2) + 9) {}^(2) + 5)`

`( - 16)(18(( - 12) - 8 + 9)) {}^(2) + 5)`

`- 16(18( - 11) {}^(2) + 5)`

`- 16(2183)`

`- 34928`