USING CHAIN RULE WITH POLYNOMIAL FUNCTIONS WORKSHEET

Problem 1 : 

(x - x² - x4)5 / 5

Solution

Problem 2 :

(5 - x)-2 / 2

Solution

Problem 3 :

(2x + 1)-1

Solution

Problem 4 :

(9 - 4x)-3

Solution

Problem 5 :

(4x2 - 3x3 + x)-2

Solution

Problem 6 :

5(x² - 9)-3

Solution

Problem 7 :

(x-1 - 2x-2)-3

Solution

Problem 8 :

(3x + 1)1/2

Solution

Problem 9 :

(6x + 1)1/3

Solution

Problem 10 :

(5x + 7)3/2

Solution

Problem 11 :

(x3 - 5x2 + x)3/4

Solution

Problem 12 :

(x5 - 5x)1/5

Solution

Answer Key

1)  (x - x² - x4)4 (1 - 2x - 4x3)

2)  (5 - x)-3

3)  -2(2x + 1)-2

4)  12 (9 - 4x)-4

5) -2(8x - 9x² + 1) / (4x² - 3x³ + x)3

6)  -30x (x² - 9)-4

7)  -3x5 (4 - x) (x - 2)-4

8) 3 / 2√(3x + 1)

9) 2(6x + 1)-2/3

10)  15(5x + 7)1/2 / 2

11)  3(3x² - 10x + 1) / 4(x³ - 5x² + x)

12)  (x4 - 1) (x5 - 5x)-4/5

Find the derivative:

Problem 1 :     

y =∜(7m³ - 4m² + 2)

Solution

Problem 2 :

c = (4k² + 3)²

Solution

Problem 3 :

r = (4w + 3)5

Solution

Problem 4:

d = 3 / √x + 2

Solution

Problem 5 :

f = 2 / √4e + 5

Solution

Problem 6 :

g(x) = 1/√1 - 2x

Solution

Problem 7 :

k(n) = 4/√n2 + 6

Solution

Problem 8  :

p(r) = 12 / (7 - r)5

Solution

Problem 9 :

q(z) = 5 / 5(z5 - 32)

Solution

Answer Key

1)  dy/dm = (21m² - 8m) / 4 (7m³ - 4m² + 2)³

2)  dc/dk = 16k / 3 (4k² + 3)

3)  dr/dw = 5 (4w + 3)

4)  dd/dx = -3/2√(x + 2)3

5)  df/de = -4/√(4e + 5)³

6)  g’(x) = 1/√(1 - 2x)³

7)  k’(n) = -4n / √(n² + 6)³

8)  p’(r) = 15 / (7 - r)9

9)  q’(z) = -5z4 / 5(z5 - 32)6

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