Asian College of Technology - Bulacao Campus
Senior High School Department
Basic Calculus STEM 03
Final Examination
Name: ________________________Year & Section: _______________ Date: ____________
Direction: Solve the given equations below and tick the capital letter of the correct answer.
(3 pts each.)
1. Find the derivative of f(x) = (x6 + 4)5
A. f '(x) = 5x5(x4 + 4)4
B. f '(x) = 6x5(x6 + 4)4
C. f '(x) = 30x5(x6 + 4)4
D. f '(x) = 30x6(x6 + 4)4
2. To find the derivative of this function you can use ________________.
A. Only the Chain Rule
B. The quotient & the Chain Rules
C. Only the Quotient Rule
D. Product & Quotient Rules
3. What is the derivative of xn?
A. (n-1)xn
B. nxn+1
C. (n+1)xn-1
D. nxn-1
4. What is the quotient rule?
A. (vu' - uv')/v2
B. (uv' - vu')/v2
C. (vu' - uv')/u2
D. (uv' - vu')/u2
5. What is the Product Rule?
A. uv' + vu'
B. uv' - vu'
C. uv - v'u'
D. v'u' – vu
6. Derivative means the same thing as ______________.
A. slope of the tangent line
B. slope of the normal line
C. exponent
D. potato
7. When do you use the chain rule?
A. anytime you want
B. when there is division
C. where there is division
D. when there is a function in a function
8. Find the derivative of f(x) = (x6 + 4)5
A. f '(x) = 5x5(x4 + 4)4
B. f '(x) = 6x5(x6 + 4)4
C. f '(x) = 30x5(x6 + 4)4
D. f '(x) = 30x6(x6 + 4)4
4𝑥 3
9. Determine the derivative of this function 2𝑥 2 −5
A.
B.
C.
D.
(8x3 -60x/(2x2-5)2
16x4/(2x2-5)2
(8x4 -60x2)/(2x2-5)2
3x/(2x2-5)2
10. Find the derivative of f(x)=(x3-2x)2
A. 6x5 - 12x3+8x
B. 6x5 - 16x3+8x
C. x6-4x4+4x2
D. 6x5 - 16x3-8x
11. Find the derivative of the given equation f(x) = x3 + x2 + 3
A. 3x2 + 2x
B. 3x + 2x
C. 3x + 2x + 3
D. x3 + x2
12. Find the second derivative of the function f (x) = 2x - 5x6
A. f ''(x)= 2 - 30x
B. f ''(x) = 2-30x5
C. f ''(x) = -30x5
D. f ''(x) = -150x4
13. Which rule would you need to use in solving the derivative of this function,
f(x) = 6√2𝑥 − 5
A. Power Rule
B. Product Rule
C. Quotient Rule
D. Chain Rule
14. What rule should be used in deriving h(x) = 2(x - 4)3
A. Chain rule
B. Product rule
C. Quotient rule
D. Power rule
15. Find the derivative of f(x) = (x2 +1)6
A. 12(x2 + 1)6
B. 12x(x2 + 1)6
C. 12x(x2 + 1)5
D. 12(x2 + 1)5
√5𝑥 2 + 2𝑥 − 7
Prepared by:
Reymart B. Saladas