Calculus · SEC2_GYM

Differentiation rules

Question 1/8+12 XP

Differentiate .

Secant becomes tangentf(x) = 5x³, x = 1

curve fsecant Δx = 0.6secant Δx = 0.3secant Δx = 0.1tangent, slope 15point of tangency

All three secants pass through (1, 5). As Δx shrinks (0.6 → 0.3 → 0.1) the secant slope moves 25.8 → 19.95 → 16.55 — towards the tangent slope f′(1) = 15. That limit is the derivative.

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