Polynomial Derivative Practice Paper 2

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Date:

📚 Part 1: Basic Power Rule

Rule: If f(x) = ax^n, then f'(x) = anx^(n-1)

1. Find the derivative of f(x) = 5x³

f'(x) = 15x²

f'(x) = 5x²

f'(x) = 15x³

f'(x) = 3x²

2. Find the derivative of g(x) = -2x⁴

3. Find the derivative of h(x) = 7x²

4. Find the derivative of k(x) = x⁶

For polynomials: Differentiate each term separately

5. Find the derivative of f(x) = 3x⁴ + 2x³ - 5x²

6. Find the derivative of g(x) = x⁵ - 4x³ + 7x - 2

7. If f(x) = 2x³ - 6x² + 4x, what is f'(2)?

Step 1: Find f'(x) = _______________

Step 2: Substitute x = 2: f'(2) = _______________

8. Find the derivative of h(x) = -x⁴ + 3x² - 8

9. A particle's position is given by s(t) = t³ - 6t² + 9t metres. Find the velocity function v(t).

10. Extension: If f(x) = ax³ + bx² + cx + d and f'(x) = 6x² - 4x + 5, find the values of a, b, and c.

a = _______, b = _______, c = _______

Success Criteria:

✓ I can apply the power rule f(x) = ax^n → f'(x) = anx^(n-1)

✓ I can differentiate polynomial functions term by term

✓ I can evaluate derivatives at specific points

Dyslexia-Friendly Note: Use different coloured pens for coefficients and exponents to help organise your work.