Q 7 - Calculus

Question

Finding antiderivatives by undoing the chain rule: For each function f that follows, find a function F with the property that F(x) = f(x). You may have to guess and check to find such a function

Step-by-Step Solution

Answer

The points for which  

Step 1: Identify the chain rule pattern

To find \( F \) such that \( F'(x) = f(x) \), look for a composite function whose derivative (via the chain rule) gives \( f(x) \).

Step 2: Guess and check

Try \( F(x) \) as an antiderivative of the outer function composed with the inner function, divided by the derivative of the inner function. Verify by differentiating.