For y = x² the derivative dy/dx is 2x and for y = x³ it is 3x², so this Year 11 sheet opens by differentiating the two basic powers. The key also records dy/dx = 0 for a constant and 3 for the gradient of a line.
Key Takeaways
dy/dx = 2x when y = x² (Q1).
dy/dx = 3x² when y = x³ (Q2).
Q3 records dy/dx = 0 for a constant.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.If y = x², what is dy/dx?
(a) x²(b) 2x(c) 2(d) 2x²
2.If y = x³, what is dy/dx?
(a) 3x²(b) x³(c) 3x(d) 6x
3.What is the gradient of the graph y = 5 at every point?
(a) 5(b) 0(c) 1(d) 5x
4.If y = 3x + 2, what is the gradient of the graph?
(a) 3(b) 2(c) 5(d) 0
5.If y = 4x³, what is dy/dx?
(a) 4x²(b) 12x²(c) 12x³(d) 3x²
6.What is the gradient of the curve y = x² at the point where x = 3?
(a) 3(b) 6(c) 9(d) 2
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Differentiate y = 5x².
8.Differentiate y = x⁴.
9.Find the gradient of y = x² at x = 2.
10.Differentiate y = 7.
11.Differentiate y = 2x³ + 3x.
12.Find dy/dx when y = x⁵.
13.Find the gradient of y = x² at x = -1.
14.Differentiate y = ½x².
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A stone is thrown so that its height is h = 30t - 5t². Find dh/dt.
16.Using the derivative h = 30t - 5t², find the speed of the stone when t = 2.
17.A cost function is C = x² + 20x. Find dC/dx.
18.Find the gradient of the curve y = x³ at x = 2.
19.A curve has equation y = x² - 4x. Find its gradient at x = 1.
20.Find the x-coordinate of the point on y = x² where the gradient is 6.
Answer Key
1. b) 2x
2. a) 3x²
3. b) 0
4. a) 3
5. b) 12x²
6. b) 6
7. Refer to solution guide.
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End of Worksheet
People Also Ask
What is dy/dx when y = x²?
2x, option (b) in this worksheet (Q1).
What is dy/dx when y = x³?
3x², option (a) in this worksheet (Q2).
What is the derivative of a constant?
0, option (b) in this worksheet (Q3).
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