G11 SUPER GIO
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LEARN MISSIONderivatives from definitions and efficient rules

derivatives from definitions and efficient rules

WORKED MODELWORKED SOURCE

Derivative from first principles

For f(x) = x^2, [f(x+h)-f(x)]/h = [(x+h)^2-x^2]/h = (2xh+h^2)/h = 2x+h. Taking h->0 gives f'(x)=2x.

  1. Expand before canceling.
  2. The quotient is defined for h != 0.
  3. Take the limit after simplification.

What is f'(3)?

MODELRate-of-Change Dial
CALC
PROVEChoose with evidence
CLUE

Pause. Find what matters. Then make your move.