For the function f(x) = sin(x) + cos(x), what is f'(π/4)? (2023)

For the function f(x) = sin(x) + cos(x), what is f'(π/4)? (2023)

Step 1: Identify the function f(x) = sin(x) + cos(x).
Step 2: Find the derivative of the function, f'(x). The derivative of sin(x) is cos(x) and the derivative of cos(x) is -sin(x). So, f'(x) = cos(x) - sin(x).
Step 3: Substitute x = π/4 into the derivative f'(x). This means we need to calculate 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 these values into the equation: f'(π/4) = √2/2 - √2/2.
Step 6: Simplify the expression: √2/2 - √2/2 = 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 – It assesses the understanding of how to substitute a value into the derivative to find the slope of the function at that point.