Chain Rule, Implicit Differentiation, Parametric Differentiation

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

1. Chain rule for y = f(u) where u = g(x) is: dy/dx =
2. For y = (3x² + 5)⁴, the derivative is:
3. Implicit differentiation applies when:
4. For x² + y² = 25, using implicit differentiation, dy/dx =
5. For x³ + y³ = 3xy, dy/dx =
6. Parametric equations x = f(t), y = g(t) give dy/dx =
7. For x = 2cos(t), y = 3sin(t), the dy/dx =
8. For parametric curve, d²y/dx² =
9. If x = e^t and y = e^(2t), then dy/dx =
10. For implicitly defined curve, the tangent slope at (x₀,y₀) is:
11. For y = (sin(x))^(cos(x)), finding dy/dx requires:
12. For x = t², y = t³, at t = 1: dy/dx =
13. The relation dy/dx = (dy/dt)/(dx/dt) requires:
14. Implicit differentiation of x²y + xy² = 1 with respect to x:
15. For e^(xy) = x + y, dy/dx =
16. Chain rule in multiple variables: If z = f(x,y), x = x(t), y = y(t), then dz/dt =
17. For sin(x+y) = xy, dy/dx =
18. The arc length element ds for parametric curve is:
19. For the curve x = a cos(t), y = a sin(t), dy/dx =
20. Implicit function theorem requires the condition:
21. For y² = x³ at (0,0), the curve has:
22. Logarithmic differentiation is useful for:
23. For y = x^x, using logarithmic differentiation: dy/dx =
24. If y = log(sin x), dy/dx equals:
25. If x = at², y = 2at, then dy/dx equals: