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‘ + βπ‘ ; ππ‘ π‘ = 4

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MAC 2233 Homework 3 Spring 2021

Name___________________________________

Show all work in the space provided. If no work is shown, the problem

οΆ Technique and rules to compute the derivative

ο· For each problem from problem 41) to 49), given π(π) compute

it derivative function π β²(π) .

41) π(π₯) = 2βπ₯2

3π₯2+1

42) π(π₯) = (π₯3 + 2π₯ β 7)(3 + π₯ β π₯2 )

43) π(π₯) = βπ₯2 + 1

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44) π(π₯) = (π₯ + 1

π₯ )

2 β

5

β3π₯

45) π(π₯) = (5π₯ 4 β 3π₯ 2 + 2π₯ + 1)10

46) π(π₯) = ( π₯+1

1βπ₯ )

2

47) π(π₯) = (3π₯ + 1)β6π₯ + 5

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48) π(π₯) = (3π₯+1)3

(1β3π₯)4

49) π(π₯) = β 1β2π₯

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 ; ππ‘ π₯ = 1

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51) π(π₯) = π₯

x2+1 ; ππ‘ π₯ = 0

52) π(π₯) = βπ₯2 + 5 ; ππ‘ π₯ = β2

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‘ 2β5

1β3t ; ππ‘ π‘ = β1

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54) π(π‘) = ( t2 β 3π‘ + 6 ) 1

2 ; ππ‘ 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‘ + βπ‘ ; ππ‘ π‘ = 4

56) π(π‘) = 2

1+π‘ 2 ; ππ‘ π‘ = 0

ο· For problem 57), 58) and 59)Find the 2nd βderivatives:

57) π(π₯) = 6π₯5 β 4π₯3 + 5π₯2 β 2π₯ + 1

π₯

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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

1βπ₯