What is the derivative of f(x) = sin(x) + cos(x)?
Correct Answer: cos(x) - sin(x)
- Step 1: Identify the function f(x) = sin(x) + cos(x).
- Step 2: Recall the derivative of sin(x), which is cos(x).
- Step 3: Recall the derivative of cos(x), which is -sin(x).
- Step 4: Apply the derivative rules: the derivative of f(x) is the derivative of sin(x) plus the derivative of cos(x).
- Step 5: Combine the results: f'(x) = cos(x) + (-sin(x)).
- Step 6: Simplify the expression: f'(x) = cos(x) - sin(x).
No concepts available.
