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What is the derivative of f(x) = sin(x) + cos(x)?

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Question: What is the derivative of f(x) = sin(x) + cos(x)?

Options:

  1. cos(x) - sin(x)
  2. -sin(x) - cos(x)
  3. sin(x) + cos(x)
  4. -sin(x) + cos(x)

Correct Answer: cos(x) - sin(x)

Solution: 

Using the derivatives of sine and cosine, f\'(x) = cos(x) - sin(x).

What is the derivative of f(x) = sin(x) + cos(x)?

Practice Questions

Q1
What is the derivative of f(x) = sin(x) + cos(x)?
  1. cos(x) - sin(x)
  2. -sin(x) - cos(x)
  3. sin(x) + cos(x)
  4. -sin(x) + cos(x)

Questions & Step-by-Step Solutions

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).
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