Example 1 · level 1
If f(x) = 6x² + 9x − 7, find f′(2).
Show solution
- f′(x) = 12x + 9.
- f′(2) = 33.
Answer: 33
CLASS 11 MATHS · LIMITS AND DERIVATIVES
Derivatives of polynomials at a point
d/dx (xⁿ) = nxⁿ⁻¹, the derivative of a constant is 0, and derivatives add term by term. Product rule: (uv)′ = u′v + uv′.
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Worked examples
Example 2 · level 2
If f(x) = 4x³ + 6x² − 6x, find f′(−1).
Show solution
- f′(x) = 12x² + 12x − 6.
- f′(−1) = −6.
Answer: -6
Example 3 · level 3
If f(x) = (2x + 2)(2x² + 4), find f′(2).
Show solution
- At x = 2: u = 6, v = 12, u′ = 2, v′ = 8.
- f′(2) = 2 × 12 + 6 × 8 = 72.
Answer: 72