USING PRODUCT RULE AND QUOTIENT RULE TO FIND DERIVATIVES WORKSHEET

Differentiate on paper without simplification:

Problem 1 :

(x + 2) (x² - 2x + 7)

Solution

Problem 2 :

(1 - x³) (7x + 4)

Solution

Problem 3 :

(3x - 5) (x³ + 2x² - 8)

Solution

Problem 4 :

(x² - 2) (5x - x³)

Solution

Problem 5 :

(x² + 3x - 1) (x³ - 4x + 7)

Solution

Problem 6 :

(x³ - 2x + 8) (6 - 5x)

Solution

Problem 7 :

(8x² - 5x) (13x² - 4)

Solution

Problem 8 :

(x⁵ - 2x³) (7x² + x - 8)

Solution

Problem 9 :

(3 - x³) (8x + 1)

Solution

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