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

Problem 2 :

y = (x³ - 2) / x

Problem 3 :

y = (x³ - 2) / x

Problem 4 :

y = (x³ - 4x² + 3x - 2)/x²

Problem 5 :

y = (3x⁷ - 7x + 11)/2x³

Problem 6 :

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

Problem 7 :

y = (x + 6)/x³

Problem 8 :

y = (2x³ + x + 4)/2x⁵

Problem 9 :

y = (x - 3)/√x

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)