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Derivative from First Principles

Mathematics · Class 12

f'(x)=lim(h->0)[f(x+h)-f(x)]/h measures instantaneous rate of change.

Derivative from first principles
rule
worked example
Derivative from first principles: f'(x)=lim(h->0)[f(x+h)-f(x)]/h measures instantaneous rate of change.
CONCEPT AND RULE: f'(x)=lim(h->0)[f(x+h)-f(x)]/h measures instantaneous rate of change.
METHOD: For derivative from first principles, identify the given information and required result. Select the
f'(x)=lim(h->0)[f(x+h)-f(x)]/h measures instantaneous rate of change.
Worked pattern: For f(x)=x^2, expansion gives f'(x)=2x.

Right triangle — Derivative from First Principles — original sketch for this lesson (not copied from a textbook).