Basic Derivatives Quiz

1. What is the derivative of f(x) = x²?

a) 2x

b) x

c) 2

d) x²

2. What is the derivative of f(x) = 3x³?

a) 3x²

b) 9x²

c) 9x³

d) 3x

3. True or False: The derivative of a constant is zero.

a) True

b) False

4. What is the derivative of f(x) = sin(x)?

a) cos(x)

b) -sin(x)

c) -cos(x)

d) sin(x)

5. What is the derivative of f(x) = e^x?

a) e^x

b) x e^x

c) e

d) 0

6. What is the derivative of f(x) = 2x using the product rule?

a) 2

b) 2x

c) 4x

d) 0

7. What is the derivative of f(x) = x * sin(x)?

a) sin(x) + x cos(x)

b) cos(x) + x sin(x)

c) sin(x) - x cos(x)

d) x sin(x)

8. True or False: The chain rule is used for composite functions.

a) True

b) False

9. What is the derivative of f(x) = (x² + 1)³?

a) 3(x² + 1)²

b) 6x(x² + 1)²

c) 6x(x² + 1)

d) 3x²(x² + 1)²

10. What is the derivative of f(x) = ln(x)?

a) 1/x

b) x

c) ln(x)

d) 1