1. h'(x) = 4(x² + 3)³(4x - 5)³(2x) + (x² + 3)⁴ * 3(4x - 5)² * 4
2. g'(x) = 10((1 + x²)/(1 - x²))⁹ * [(2x(1 - x²) - (1 + x²)(-2x))/(1 - x²)²]
3. f'(x) = 3(x + 4)²(x - 3)⁶ + (x + 4)³ * 6(x - 3)⁵
4. y' = 3(x² + 3)²(2x)(x³ + 3)² + (x² + 3)³ * 2(x³ + 3)(3x²)
5. y' = [(6x + 2)(x² + 1) - (3x² + 2x)(2x)] / (x² + 1)²
6. h'(x) = 3x²(3x - 5)² + x³ * 2(3x - 5) * 3
7. y' = 4x³(1 - 4x²)³ + x⁴ * 3(1 - 4x²)² * (-8x)
8. y' = 4((x² - 3)/(x² + 3))³ * [(2x(x² + 3) - (x² - 3)(2x))/(x² + 3)²]
9. y' = 4x³(2x - 5)⁶ + x⁴ * 6(2x - 5)⁵ * 2
10. y' = √(x² + 1) + x * (1/2)(x² + 1)^(-1/2) * 2x
11. y' = [4(2x - 5)³ * 2 * (x + 1)³ - (2x - 5)⁴ * 3(x + 1)²] / (x + 1)⁶
12. y' = 6((10x - 1)/(3x + 5))⁵ * [(10(3x + 5) - (10x - 1)(3))/(3x + 5)²]
13. y' = 3(x - 2)²(x² + 9)⁴ + (x - 2)³ * 4(x² + 9)³ * 2x
14. y' = 3(1 - x²)²(-2x)(6 + 2x)⁻³ + (1 - x²)³ * (-3)(6 + 2x)⁻⁴ * 2
15. y' = [6(3x + 5)⁴ - (6x - 1) * 4(3x + 5)³ * 3] / (3x + 5)⁸
16. y' = [3(2x² - 5)² * 4x * (x + 8)² - (2x² - 5)³ * 2(x + 8)] / (x + 8)⁴
17. f'(x) = [-12x³√(4x - 8) - (-3x⁴) * (1/2)(4x - 8)^(-1/2) * 4] / (4x - 8)
18. g'(x) = 4((2x + 5)/(6 - x²))³ * [(2(6 - x²) - (2x + 5)(-2x))/(6 - x²)²]
19. y' = 3[1/(4x + x²)³]² * [-3(4x + x²)⁻⁴ * (4 + 2x)]
Parent Tip: Review the logic above to help your child master the concept of derivative rules worksheet.
