Quiz worksheet on derivatives of trigonometric functions with multiple-choice questions and answer options.

Here’s the complete solution to Questions 1–6 from your “Derivatives of Trigonometric” quiz. I’ll explain each step clearly.

---

Question 1: What is the derivative of -cos(x)?

We know:
> The derivative of cos(x) is -sin(x)

So, derivative of -cos(x) is:
> - [derivative of cos(x)] = -(-sin(x)) = sin(x)

✔ Answer: D. sin(x)

---

Question 2: What is the derivative of tan(x)?

Standard derivative:
> d/dx [tan(x)] = sec²(x)

✔ Answer: C. sec²(x)

---

Question 3: What is the derivative of cot(x)?

Standard derivative:
> d/dx [cot(x)] = -csc²(x)

✔ Answer: D. -csc²(x)

---

Question 4: y = sin²x, find y’

This is a chain rule problem.

Let u = sin(x), then y = u²
dy/dx = dy/du * du/dx = 2u * cos(x) = 2 sin(x) cos(x)

✔ Answer: A. 2(sin x)(cos x)

*(Note: This is also equal to sin(2x), but that’s not one of the options.)*

---

Question 5: Find f’(x) if f(x) = sin⁵x

Again, chain rule.

Let u = sin(x), then f(x) = u⁵
f’(x) = 5u⁴ * cos(x) = 5 sin⁴(x) cos(x)

✔ Answer: C. 5 sin⁴x cos x

---

Question 6: Find y’ if y = 10 sin(x) + 3 cos(x)

Differentiate term by term:

- d/dx [10 sin(x)] = 10 cos(x)
- d/dx [3 cos(x)] = 3 (-sin(x)) = -3 sin(x)

So, y’ = 10 cos(x) - 3 sin(x)

✔ Answer: B. 10cos(x) - 3sin(x)

*(Note: Option D is “10cos(x) - 3cos(x)” — that’s incorrect.)*

---

## ✔ Final Answers:

1. D
2. C
3. D
4. A
5. C
6. B

---

Let me know if you’d like help with Questions 7–10 (which are cut off in the image)!