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Calculus
· Examples✏️ Worked Examples — Step by Step
E1
EasyDifferentiate f(x) = 4x³ − 2x + 7
💡 Power rule term-by-term.
👁 Show Solution
f'(x) = 4·3x² − 2 + 0 = 12x² − 2. ✅ Answer: 12x² − 2
✅12x² − 2
E2
Medium∫ (3x² + 2x) dx
💡 Reverse power rule.
👁 Show Solution
∫3x² dx + ∫2x dx = x³ + x² + C. ✅ Answer: x³ + x² + C
✅x³ + x² + C
E3
Challengingd/dx [x² · sin x] (product rule)
💡 (uv)′ = u′v + uv′.
👁 Show Solution
u = x², v = sin x → u'v + uv' = 2x · sin x + x² · cos x. ✅ Answer: 2x sin x + x² cos x
✅2x sin x + x² cos x