# DERIVATIVE USING POWER RULE WORKSHEET

Find dy/dx if :

Problem 1 :

y = x + √x

Solution

Problem 2 :

y = x5 - 3√x

Solution

Problem 3 :

y = x5/2 - 2/x

Solution

Problem 4 :

y = 3x4 - 2/x + 6/x2

Solution

Problem 5 :

y = (x + 5) (x + 2)

Solution

Problem 6 :

y = (3x + 1) (5x - 3)

Solution

Problem 7 :

y = (5x² - 3) (4x³ + x)

Solution

Problem 8 :

y = (x3 + 1) (2x + 3)

Solution

Problem 9 :

y = (x5 - 2x)2

Solution

Problem 10 :

y = (x - 2) (x + 1) (3x + 1)

Solution

Problem 11 :

y = (x - a)³

Solution

Problem 12 :

y = (2x + 3)³

Solution

Problem 13 :

y = 2x (3x² - 7x + 8)

Solution

Problem 14 :

y = 3x² (x + 1) (x - 2)

Solution

Problem 15 :

y = (x + 1/x)²

Solution

1)  dy/dx = 1 + 1/2√x

2)  dy/dx = 5x4 - 3/2√x

3)  dy/dx = 5/2 x3/2 + 2/x2

4)  dy/dx = 12x³ + 2/x² - 12/x³

5)  dy/dx = 2x + 7

6)  dy/dx = 30x - 4

7)  dy/dx = 100x4 - 21x2 - 3

8)  dy/dx = 8x3 + 9x2 + 2

9)  dy/dx = 10x9 - 24x5 + 8x

10)  dy/dx = 9x² - 4x - 7

11)  dy/dx = 3x² - 6xa + 3a²

12)  dy/dx = 24x² + 72x + 54

13)  dy/dx = 18x² - 28x + 16

14)  dy/dx = 12x³ - 9x² - 12x

15)  dy/dx = 2x - 2/x3

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