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DifferentiationIEB Grade 12 Maths, Paper 1

From first principles:

f′(x) = lim (h→0) [f(x+h) − f(x)] ÷ h

Power rule: d/dx (xⁿ) = n·xⁿ⁻¹

Example: f(x) = 3x² − 4x + 1

f′(x) = 6x − 4

Gradient of tangent at x = 2:

m = f′(2) = 8 so y − 5 = 8(x − 2)

Exam tip: always show the limit step.

DifferentiationIEB Grade 12 Maths, Paper 1

From first principles:

f′(x) = lim (h→0) [f(x+h) − f(x)] ÷ h

Power rule: d/dx (xⁿ) = n·xⁿ⁻¹

Example: f(x) = 3x² − 4x + 1

f′(x) = 6x − 4

Gradient of tangent at x = 2:

m = f′(2) = 8 so y − 5 = 8(x − 2)

Exam tip: always show the limit step.

Thandi Mokoena

Ridgeview College

Maths 95%

Calculus and functions: full summary

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