Final answer:
To find g'(x) using part 1 of the fundamental theorem, we need to first find the antiderivative of g(x). Alternatively, we can use the chain rule to find g'(x).
Step-by-step explanation:
To find g'(x) using part 1 of the fundamental theorem, we need to first find the antiderivative of g(x). Let's assume that g(x) = the integral of f(t) dt from a to x, where f(t) is a continuous function. According to the fundamental theorem of calculus, if F(x) is an antiderivative of f(x), then the derivative of the integral from a to x of f(t) dt with respect to x is f(x). Therefore, g'(x) = f(x).
Alternatively, we can use the chain rule to find g'(x). Let's assume that g(x) = F(u(x)), where F(x) is an antiderivative of f(x) and u(x) is a differentiable function. By the chain rule, g'(x) = F'(u(x)) * u'(x), where F'(u(x)) is the derivative of F(x) with respect to x evaluated at u(x) and u'(x) is the derivative of u(x) with respect to x.