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Find the derivative of g(x) = sin(x) + cos(x). (2020)

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Question: Find the derivative of g(x) = sin(x) + cos(x). (2020)

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)

Exam Year: 2020

Solution: 

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

Find the derivative of g(x) = sin(x) + cos(x). (2020)

Practice Questions

Q1
Find the derivative of g(x) = sin(x) + cos(x). (2020)
  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 g(x) = sin(x) + cos(x). (2020)
  • Step 1: Identify the function g(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: g'(x) = derivative of sin(x) + derivative of cos(x).
  • Step 5: Substitute the derivatives: g'(x) = cos(x) + (-sin(x)).
  • Step 6: Simplify the expression: g'(x) = cos(x) - sin(x).
  • Derivative of Trigonometric Functions – Understanding how to differentiate sine and cosine functions.
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