Chain Rule & Implicit Differentiation

Grade 12 Maths — Chain Rule & Implicit Differentiation: 25 practice questions with instant scoring and explanations.

1. The chain rule states that if y = f(g(x)), then dy/dx equals:
2. If y = (3x² + 1)⁵, then dy/dx equals:
3. For y = sin(x²), the derivative dy/dx is:
4. For y = e^(2x), the derivative is:
5. The derivative of y = ln(x² + 1) is:
6. If y = √(5x + 3), then dy/dx equals:
7. For implicit differentiation of x² + y² = 25, we get dy/dx equals:
8. For the equation x³ + y³ = 6xy, using implicit differentiation gives dy/dx as:
9. Implicit differentiation is used when:
10. For the equation y = cos(e^x), the derivative is:
11. If y = (x² + 1)³(x³ + 2)², then by chain rule and product rule, dy/dx involves:
12. For y = tan(x³), dy/dx equals:
13. Differentiating x² + 2xy + y² = 5 implicitly gives dy/dx as:
14. For y = sin⁻¹(2x), dy/dx equals:
15. The chain rule can be extended to: If y = f(u) and u = g(v) and v = h(x), then dy/dx equals:
16. For y = e^(sin(x)), the derivative is:
17. If x² + xy + y² = 3, then dy/dx at the point (1, 1) is:
18. For differentiation of y = [f(x)]^n, dy/dx equals:
19. The derivative of y = ln(sin(x)) is:
20. For y = (x² − 1)/(x² + 1), the derivative can be found using:
21. Implicit differentiation of y² = 4x gives dy/dx as:
22. For y = √(1 − x²), the derivative is:
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