Step 1: Identify the function f(x) = sin(x) + cos(x).
Step 2: Find the derivative of f(x), which is f'(x) = cos(x) - sin(x).
Step 3: Substitute x = π/4 into the derivative: f'(π/4) = cos(π/4) - sin(π/4).
Step 4: Calculate cos(π/4) and sin(π/4). Both are equal to √2/2.
Step 5: Substitute the values into the equation: f'(π/4) = √2/2 - √2/2.
Step 6: Simplify the expression: f'(π/4) = 0.
Differentiation of Trigonometric Functions – The question tests the ability to differentiate the function f(x) = sin(x) + cos(x) and evaluate the derivative at a specific point.
Evaluation of Derivatives – The question requires evaluating the derivative at x = π/4, which involves knowing the values of sin(π/4) and cos(π/4).
