Calculus Assignments
MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE
MAC 2233 SPRING 2021
MAC 2233 Homework 3 Spring 2021
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Show all work in the space provided. If no work is shown, the problem
will receive at most half credit for a correct answer.
οΆ Technique and rules to compute
the derivative
ο· For each problem from problem 41) to 49), given π(π) compute
it derivative function π β²(π) .
41) π(π₯) =
2βπ₯
2
3π₯
2+1
42) π(π₯) = (π₯
3 + 2π₯ β 7)(3 + π₯ β π₯
2
)
43) π(π₯) = βπ₯
2 + 1
MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE
MAC 2233 SPRING 2021
44) π(π₯) = (π₯ +
1
π₯
)
2
β
5
β3π₯
45) π(π₯) = (5π₯
4 β 3π₯
2 + 2π₯ + 1)
10
46) π(π₯) = (
π₯+1
1βπ₯
)
2
47) π(π₯) = (3π₯ + 1)β6π₯ + 5
MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE
MAC 2233 SPRING 2021
48) π(π₯) =
(3π₯+1)
3
(1β3π₯)
4
49) π(π₯) = β
1β2π₯
3π₯+2
ο· From problem 50) to 52) find the equation of
The Tangent-Line for given function π(π₯) at a given π₯ = π.
50) π(π₯) = π₯
2 β 3π₯ + 2 ; ππ‘ π₯ = 1
MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE
MAC 2233 SPRING 2021
51) π(π₯) =
π₯
x
2+1
; ππ‘ π₯ = 0
52) π(π₯) = βπ₯
2 + 5 ; ππ‘ π₯ = β2
ο· For problem 53) and 54) Find the rate of change of π(π)
with respect to π at the given value of π .
53) π(π‘) =
2π‘
2β5
1β3t
; ππ‘ π‘ = β1
MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE
MAC 2233 SPRING 2021
54) π(π‘) = ( t
2 β 3π‘ + 6 )
1
2 ; ππ‘ π‘ = 1
ο· For problem 55) and 56) Find the Percentage-Rate of
change of π(π) with respect to π at the given value
of π .
55) π(π‘) = π‘
2 β 3π‘ + βπ‘ ; ππ‘ π‘ = 4
56) π(π‘) =
2
1+π‘
2
; ππ‘ π‘ = 0
ο· For problem 57), 58) and 59)Find the 2nd
βderivatives:
57) π(π₯) = 6π₯
5 β 4π₯
3 + 5π₯
2 β 2π₯ +
1
π₯
MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE
MAC 2233 SPRING 2021
58) π(π₯) =
2
1+π₯
2
59) π(π₯) = (3π₯
2 + 2)
4
60) For the function π(π₯) given below,
Find the nth-derivative π
(π)(π₯) .
π(π₯) =
1
1βπ₯