lightbulb Key Concepts

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1. Definition of Derivative

The derivative of f(x) at x = a is the slope of the tangent to the curve at that point.

f'(x) = lim (h→0) [f(x+h) - f(x)] / h

2. Differentiation Rules

• Product Rule: (uv)' = u'v + uv'
• Quotient Rule: (u/v)' = (u'v - uv') / v²
• Chain Rule: d/dx [f(g(x))] = f'(g(x)) · g'(x)

3. Standard Derivatives

• d/dx (xⁿ) = nxⁿ⁻¹
• d/dx (sin x) = cos x
• d/dx (cos x) = -sin x
• d/dx (eˣ) = eˣ
• d/dx (log x) = 1/x