Final answer:
The derivative of g(x) = ex³ - 2x is 3ex² - 2.
Step-by-step explanation:
To find the derivative of the function g(x) = ex³ - 2x, we can use the power rule and the constant rule for derivatives.
The power rule states that if we have a term of the form
, the derivative is
.
In this case, the derivative of ex³ is 3ex².
The derivative of the second term, -2x, is simply -2.
Therefore, the derivative of g(x) is 3ex² - 2.