Final answer:
The derivative of the given function is (9x² - 4x + 8)eˣ³. The correct option is b) (9x²−4x+8)eˣ³
Step-by-step explanation:
The derivative of the function y = (3x³ - 2x² + 8x - 6)eˣ³ can be found using the product rule and chain rule of differentiation.
First, apply the product rule by differentiating the function inside the parentheses and leaving the exponential function unchanged. The derivative of (3x³ - 2x² + 8x - 6) with respect to x is 9x² - 4x +8.
Next, apply the chain rule by multiplying the derivative of the exponent eˣ³, which is 3x², with the original function. Therefore, the derivative of y = (3x³ - 2x² + 8x - 6)eˣ³ is (9x² - 4x + 8)eˣ³.
The correct option is b) (9x²−4x+8)eˣ³