Question

Evaluate dydx at x=2 for the function below. y=6u^3+5u+2, where u=−3x^2−4x+9

Answer 1

Step-by-step 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.

$\frac{dy}{dx} = 6(3)( - 3 {x}^{2} - 4x + 9) {}^{2} ( - 6x - 4) + 5( - 6x - 4)$

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

Factor out -6x-4,

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

Know plug in x=-2 to evaluate the derivative

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

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

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

$- 16(2183)$

$- 34928$