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Find the derivative of f(x) = sin(x) + cos(x).

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Question: Find 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. -cos(x) + sin(x)

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

Solution: 

The derivative f\'(x) = d/dx(sin(x) + cos(x)) = cos(x) - sin(x).

Find the derivative of f(x) = sin(x) + cos(x).

Practice Questions

Q1
Find 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. -cos(x) + sin(x)

Questions & Step-by-Step Solutions

Find the derivative of f(x) = sin(x) + cos(x).
  • 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.
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