DERIVATIVE OF RATIONAL FUINCTION WITHOUT USING QUOTIENT RULE WORKSHEET

Here we see derivatives of rational functions without using quotient rule.

Problem 1 :

y = (2x + 5) / x

Solution

Problem 2 :

y = (x³ - 2) / x

Solution

Problem 3 :

y = (x³ - 2) / x

Solution

Problem 4 :

y = (x3 - 4x2 + 3x - 2)/x2

Solution

Problem 5 :

y = (3x7 - 7x + 11)/2x3

Solution

Problem 6 :

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

Solution

Problem 7 :

y = (x + 6)/x3

Solution

Problem 8 :

y = (2x3 + x + 4)/2x5

Solution

Problem 9 :

y = (x - 3)/√x

Solution

Answer Key

1) dy/dx = -5/x2

2) dy/dx = (2/x) + 2/x2

3)  dy/dx = 1 - (7/x2)

4)  dy/dx = 1 - (3/x2) + (4/x3)

5)  dy/dx = 6x3 + (7/x3) - (33/2x4)

6)  dy/dx = 4 + (9/x2)

7)  dy/dx = (-2/x3) - (18/x4)

8)  dy/dx = (-2/x3) - (5/2x6) - (10/x6)

9)  dy/dx = (2/√x) + (3/2x√x)

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