Let g(x) be an antiderivative for f(x). Then ln(1+(g(x))^2) is an antiderivative for
Step-by-Step Solution
Key Concept: Differentiate the given function ln(1+(g(x))^2) with respect to x using the chain rule, knowing that g'(x) = f(x).
Let y = ln(1+(g(x))^2). Differentiating with respect to x, we get dy/dx = (1 / (1+(g(x))^2)) * d/dx(1+(g(x))^2) = (1 / (1+(g(x))^2)) * 2g(x) * g'(x). Since g'(x) = f(x), dy/dx = 2f(x)g(x) / (1+(g(x))^2).
Correct Answer: 2