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If f(x) = sin(x) + cos(x), what is f'(x)?

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Question: If f(x) = sin(x) + cos(x), what is f\'(x)?

Options:

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

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

Solution: 

Using the derivative rules, f\'(x) = cos(x) - sin(x).

If f(x) = sin(x) + cos(x), what is f'(x)?

Practice Questions

Q1
If f(x) = sin(x) + cos(x), what is f'(x)?
  1. cos(x) - sin(x)
  2. -sin(x) + cos(x)
  3. sin(x) + cos(x)
  4. -cos(x) - sin(x)

Questions & Step-by-Step Solutions

If f(x) = sin(x) + cos(x), what is f'(x)?
  • Step 1: Identify the function f(x) = sin(x) + cos(x).
  • Step 2: Recall the derivative rules for sine and cosine functions.
  • Step 3: The derivative of sin(x) is cos(x).
  • Step 4: The derivative of cos(x) is -sin(x).
  • Step 5: Apply the derivative rules to f(x): f'(x) = d/dx[sin(x)] + d/dx[cos(x)].
  • Step 6: Substitute the derivatives: f'(x) = cos(x) + (-sin(x)).
  • Step 7: Simplify the expression: f'(x) = cos(x) - sin(x).
  • Derivative of Trigonometric Functions – Understanding how to differentiate sine and cosine functions.
  • Sum Rule of Derivatives – Applying the sum rule to find the derivative of a function that is the sum of two other functions.
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