Example 1 · level 1
f(x) = (3x − 5)². Find f′(0).
Show solution
- f′(x) = 2(3x − 5) × 3.
- f′(0) = 2 × (−5) × 3 = −30.
Answer: -30
CLASS 12 MATHS · CONTINUITY AND DIFFERENTIABILITY
Derivative by the chain rule at a point
d/dx [g(x)]ⁿ = n[g(x)]ⁿ⁻¹ × g′(x). Differentiate the outer function, keep the inside, then multiply by the derivative of the inside.
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Worked examples
Example 2 · level 2
f(x) = (−x² + 4)³. Find f′(−2).
Show solution
- f′(x) = 3(−x² + 4)² × −2x.
- f′(−2) = 3 × (0)² × −2 × (−2) = 0.
Answer: 0
Example 3 · level 3
f(x) = √(4x). Find f′(4).
Show solution
- f′(x) = 4/(2√(4x)).
- f′(4) = 4/(2 × 4) = 1/2.
Answer: 1/2