Quiz on trigonometric derivatives featuring 11 questions with multiple-choice answers.

I'll work through each question step by step to find the correct answers.

Question 1: d/dx(cos x)
- The derivative of cos(x) is -sin(x)
- Answer: D (-sin x)

Question 2: d/dx(tan x)
- The derivative of tan(x) is sec²(x)
- Answer: C (sec² x)

Question 3: d/dx(csc x)
- The derivative of csc(x) is -csc(x)cot(x)
- Answer: C (-csc x cot x)

Question 4: d/dx(x - 3 sin x)
- Derivative of x is 1
- Derivative of -3 sin(x) is -3 cos(x)
- Result: 1 - 3 cos(x)
- Answer: B (1 - 3 cos x)

Question 5: d/dx(x sin x)
- This requires the product rule: (uv)' = u'v + uv'
- Let u = x, so u' = 1
- Let v = sin(x), so v' = cos(x)
- Result: 1·sin(x) + x·cos(x) = sin(x) + x cos(x)
- Answer: A (x cos x + sin x)

Question 6: d/dx(sin x + cos x)
- Derivative of sin(x) is cos(x)
- Derivative of cos(x) is -sin(x)
- Result: cos(x) - sin(x)
- Looking at the options, this equals -sin(x) + cos(x)
- Answer: B (-sin x + cos x)

Final Answer:
1. D
2. C
3. C
4. B
5. A
6. B