GRE Subject 2026 Practice Test Maths Calculus Free Quiz 2

11. What is the product rule for differentiation?

A. f'g - fg' B. f/g C. f'g + fg' D. f'g'

12. What is the quotient rule for differentiation?

A. (f'g + fg')/g^2 B. (f'g - fg')/g C. (f'g)/g^2 D. (f'g - fg')/g^2

13. What is the derivative of cot(x)?

A. sec^2(x) B. -sec^2(x) C. -csc^2(x) D. csc(x)cot(x)

14. What rule is used to evaluate limits of indeterminate forms?

A. Product rule B. Quotient rule C. Chain rule D. L'Hopital's rule

15. What is ∫(1/x) dx?

A. x + C B. ln|x| + C C. e^x + C D. x^2 + C

16. What is integration by parts?

A. ∫u dv = uv - ∫v du B. ∫u dv = uv + ∫v du C. ∫u dv = u/v D. ∫u dv = uv

17. What is the derivative of sec(x)?

A. sec^2(x) B. -csc^2(x) C. csc(x)cot(x) D. sec(x)tan(x)

18. What is ∫sec^2(x) dx?

A. tan(x) + C B. cot(x) + C C. sec(x) + C D. csc(x) + C

19. What is the derivative of arctan(x)?

A. 1/√(1-x^2) B. 1/(1-x^2) C. 1/(1+x^2) D. -1/(1+x^2)

20. What is the derivative of arcsin(x)?

A. 1/(1+x^2) B. -1/√(1-x^2) C. 1/√(x^2-1) D. 1/√(1-x^2)