Given that f'(3) = 6 and g'(3) = -2 find (f+g)'(3).

Verified step by step guidance

1. Step 1: Understand the problem. We are given the derivatives of two functions, f and g, at x = 3. Specifically, f'(3) = 6 and g'(3) = -2. We need to find the derivative of the sum of these functions, (f+g)'(3).
2. Step 2: Recall the rule for the derivative of a sum. The derivative of the sum of two functions is the sum of their derivatives. Mathematically, this is expressed as (f+g)'(x) = f'(x) + g'(x).
3. Step 3: Apply the rule to the given point. Substitute x = 3 into the formula: (f+g)'(3) = f'(3) + g'(3).
4. Step 4: Substitute the given values. We know f'(3) = 6 and g'(3) = -2, so substitute these values into the equation: (f+g)'(3) = 6 + (-2).
5. Step 5: Simplify the expression. Combine the values to find the derivative of the sum at x = 3.