Step 1: Identify the function you want to differentiate, which is f(x) = sin(x) + cos(x).
Step 2: Recall the derivative rules for sine and cosine functions: the derivative of sin(x) is cos(x) and the derivative of cos(x) is -sin(x).
Step 3: Apply the derivative rules to each part of the function: the derivative of sin(x) is cos(x) and the derivative of cos(x) is -sin(x).
Step 4: Combine the results from Step 3: f'(x) = cos(x) - sin(x).
Differentiation of Trigonometric Functions – The question tests the ability to differentiate basic trigonometric functions, specifically sine and cosine.
Sum Rule in Differentiation – The question also tests the application of the sum rule, which states that the derivative of a sum is the sum of the derivatives.
