Final answer:
To find the derivative of the function g(x) = (x² + 2x + 3)eˣ, use the product rule. The derivative is (x² + 4x + 5)eˣ.
Step-by-step explanation:
To find the derivative of the function g(x) = (x² + 2x + 3)eˣ, we can use the product rule. The product rule states that the derivative of a product of two functions is equal to the derivative of the first function times the second function, plus the first function times the derivative of the second function. Applying this rule to the given function, we have:
g'(x) = (2x + 2)(x² + 2x + 3)eˣ + (x² + 2x + 3)eˣ
Simplifying this expression gives:
g'(x) = (2x + 2 + x² + 2x + 3)eˣ
g'(x) = (x² + 4x + 5)eˣ