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Math Learning PlatformDifferential Calculus — Limits and Derivatives
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📖 About this lesson
Introduction to limits of functions and the concept of derivatives
Lesson Content
Differential Calculus
Limits
lim(x→a) f(x) = value f(x) approaches as x → a
Derivatives
f'(x) = instantaneous rate of change
Key rules
- •(xⁿ)' = nxⁿ⁻¹
- •(sin x)' = cos x
- •(eˣ)' = eˣ
- •Product rule: (fg)' = f'g + fg'
- •Chain rule: (f∘g)' = f'(g(x))·g'(x)
Practical Examples
1
Example 1
📋 Problem
Trouver la dérivée de f(x) = 3x² + 5x - 2
✅ Solution
f'(x) = 6x + 5
💡 Explanation
Dérivée de 3x² = 3·2x = 6x, dérivée de 5x = 5, dérivée de -2 = 0
2
Example 2
📋 Problem
Trouver f'(x) pour f(x) = sin(x)·eˣ
✅ Solution
f'(x) = cos(x)·eˣ + sin(x)·eˣ
💡 Explanation
Règle du produit : (fg)' = f'g + fg' avec f=sin(x) et g=eˣ
Ready to Practice? 💪
4 exercise(s) available for this lesson
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