Find the derivative of f(x) = sin(x) + cos(x) at x = π/4.

Find the derivative of f(x) = sin(x) + cos(x) at x = π/4.

Step 1: Identify the function we need to differentiate, which is f(x) = sin(x) + cos(x).
Step 2: Find the derivative of f(x). The derivative of sin(x) is cos(x) and the derivative of cos(x) is -sin(x).
Step 3: Combine the derivatives: f'(x) = cos(x) - sin(x).
Step 4: Now, we need to evaluate the derivative at x = π/4.
Step 5: Substitute π/4 into the derivative: f'(π/4) = cos(π/4) - sin(π/4).
Step 6: Calculate cos(π/4) and sin(π/4). Both are equal to √2/2.
Step 7: Substitute these values into the equation: f'(π/4) = √2/2 - √2/2.
Step 8: Simplify the result: f'(π/4) = 0.

Differentiation of Trigonometric Functions – The question tests the ability to differentiate basic trigonometric functions, specifically sine and cosine.
Evaluation of Derivatives at Specific Points – The question requires evaluating the derivative at a specific point, which tests understanding of both differentiation and substitution.