QUOTIENT RULE USING DERIVATIVES WORKSHEET

Differentiate mentally without simplification:

Problem 1 :

x / (2x - 1)

Solution

Problem 2 :

x³ / (x² - 4)

Solution

Problem 3 :

(x + 4) / (x - 6)

Solution

Problem 4 :

(2x + 5) / (4x - 3)

Solution

Problem 5 :

x / (2x² - 8)

Solution

Problem 6 :

(x - 7) / x²

Solution

Problem 7 :

(x² + 4x - 1) / (x + 3)

Solution

Problem 8 :

(x² - 9x + 11) / (2x + 5)

Solution

Problem 9 :

(3x - 1) / (x² + 12)

Solution

Problem 10 :

(6x + 7) / (x² - x + 3)

Solution

Problem 11 :

(x³ + x) / (x² - x - 1)

Solution

Problem 12 :

(5x² - 2x) / (3x + 1)

Solution

Answer Key

1)  -2 / (2x - 1)²

2)  (x4 - 12x²) / (x² - 4)²

3)  - 10 / (x - 6)²

4)  -26 / (4x - 3)²

5)  -(8 + 2x²) / (2x² - 8)² 

6)  (14 - x) / x3

7)  (x2 + 6x + 13) / (x + 3)²

8)   (2x+ 10x - 67) / (2x + 5)²

9)   (-3x² + 38) / (x² + 12)²

10)  (15x² + 10x- 2) / (3x + 1)²

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