6/13/23, 8:14 AM BASIC CALCULUS FINAL EXAM
BASIC CALCULUS FINAL EXAM
30 questions
1. The process of finding the derivative is called.
A. Derivatives
B. Integral
C. Integration
D. Differentiation
2. The function that gives the general formula for the slope f and is denoted by f' (read as "f
prime") is called.
A. Integration
B. Derivatives
C. Differentiation
D. Integral
3. If f(x) = c, then f(x)=0.
A. Constant Multiple Rule
B. Sum Rule
C. Constant Rule
D. Power Rule
4. If f(x) = xn , then f(x) = nxn − 1.
A. Constant Multiple Rule
B. Difference Rule
C. Power Rule
D. Constant Rule
5. If f(x) = k * h(x), then f(x) = k * the derivative of h(x).
A. Sum and Difference Rule
B. Power Rule
C. Constant Multiple Rule
D. Constant Rule
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6/13/23, 8:14 AM BASIC CALCULUS FINAL EXAM
6. If f(x) = g(x) +h(x) where g and h are differentiable functions, then f(x) = the derivative of
g(x) +the derivative of h(x).
A. Difference Rule
B. Product Rule
C. Quotient Rule
D. Sum Rule
7. If f(x) = g(x) - h(x) where g and h are differentiable functions, then f(x) = the derivative of
g(x) - the derivative of h(x).
A. Sum Rule
B. Product Rule
C. Quotient Rule
D. Difference Rule
8. If f(x) = (uv), then udv + vdu.
A. Product Rule
B. Quotient Rule
C. Sum Rule
D. Difference Rule
9. If f(x) = (u/v), then (vdu - udv) divided by v 2 .
A. Quotient Rule
B. Product Rule
C. Difference Rule
D. Sum Rule
10. If y is a differentiable function of u and u is a differentiable function of x, then y can be
regarded as a function of x, and that
dy/dx=dy/du (du/dx). That is, the derivative of y with respect to x is the derivative of y with
respect to u multiplied by the derivative of u with respect to x.
A. Implicit Differentiation
B. Higher - Order Derivatives
C. Chain Rule
D. Antiderivative
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6/13/23, 8:14 AM BASIC CALCULUS FINAL EXAM
11. A function that you can further compute the derivative of the derivative. Suppose that you
start with a function f and compute its first derivative f’. You can still compute its second
derivative f”, its third derivative f”’, and so on.
A. Implicit Differentiation
B. Higher - Order Derivatives
C. Chain Rule
D. Antiderivative
12. The process involves differentiating each term of an equation on both sides, including
those that contain the variable y.
A. Chain Rule
B. Antiderivative
C. Implicit Differentiation
D. Higher - Order Derivatives
13. The derivative of sin u
A. -sin u du
B. -csc^2 u du
C. cos u du
D. sec^2 u du
14. The derivative of cos u
A. -csc^2 u du
B. sec^2 u du
C. -sin u du
D. sec^2 u du
15. The derivative of tan u
A. −csc2 u du
B. sec2 u du
C. -sin u du
D. −csc2 cot u du
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6/13/23, 8:14 AM BASIC CALCULUS FINAL EXAM
16. The derivative of cot u
A. sec2 u du
B. −csc2 u du
C. -csc u cot u du
D. -sin u du
17. The derivative of csc u
A. -sin u du
B. -csc u cot u du
C. -csc^2 u du
D. sec^2 u du
18. The derivative of sec u
A. -csc^2 u du
B. sec u tan u du
C. -sin u du
D. sec^2 u du
19. The inverse of differentiation or the process of finding the antiderivatives.
A. Antidifferentiation
B. Integration
C. Derivatives
D. Differentiation
20. The symbol ∫, denotes the operation of antidiffrentiation.
A. Epsilon
B. Integrand
C. Integral Sign
D. Summation Notation
21. What is the derivatives of square root of x?
A. 1/4x1 /2
B. 1/2x1 /4
C. 1/4x1 /4
D. 1/2x1 /2
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6/13/23, 8:14 AM BASIC CALCULUS FINAL EXAM
22. What is the derivatives of 3/4 x8 ?
A. 24 x7 ?
B. 6x7
C. 28 x7 ?
D. 26/4 x7 ?
23. What is the derivative of 3x4 + 5x2 + 101
A. 12x3 + 10x +101
B. 12x3 + 10x2 +101
C. 12x3 + 10x
D. 12x3 + 10x2
24. What is the derivative of (3x2 - 4) (x2 - 3x)?
A. 12x3 - 27x2 - 8x +12
B. 3x4 - 9x3 - 4x2 +12x
C. 3x3 - 9x2 - 4x
D. 12x2 - 27x - 8x
25. What is the derivative of(3x2 − 5)3 ?
A. (9x5 − 5)3
B. 18x(16x)2
C. (9x6 − 5)2
D. 18x(3x2 − 5)2
26. What is the second derivative of (3x2 - 4) (x2 - 3x)?
A. 3x4 − 9x3 − 4x2 + 12x
B. 36x2 - 54x - 8
C. 12x3 − 27x2 − 8x + 12
D. 72x − 54
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6/13/23, 8:14 AM BASIC CALCULUS FINAL EXAM
27. What is the derivative of sinx/(1 + cosx)?
A. 1/(1 + sinx)
B. cos/(1 + sinx)
C. 1/(1 + cosx)
D. 2cos/(1 + sinx)
28. What is the anti derivatives of ∫ 1/x6 dx?
A. -1/5x5 + C
B. 1/5x5 + C
C. -1/x7 + C
D. 1/x7 + C
29. What is the anti derivatives of ∫ 4*(square root of x) dx?
A. 8u3 /(2/3) + C
B. 4u3 /(2/3) + C
C. 4*(cube root of x) + C
D. 4*(cube root of x2 ) + C
30. What is the anti derivatives of ∫ x6 dx?
A. 6x5 + C
B. x7 + 7x + C
C. x7 + C
D. x7 /7 + C
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