LEARN · EXPLAIN · REVISE

Find the derivative of x² at x=t from the limit.

Read the idea, work independently, then explain what changed.

TOPIC 01

Derivatives and their applications: mixed review

A mixed assessment: identify the method, justify it and revise your reasoning.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Your turn

t=20

The difference quotient uses h≠0; differentiability requires a finite common two-sided limit.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Differentiate the specified function and substitute only after differentiating.

Hint 2

Use this intermediate relation.

[(t+h)^2-t^2]/h=2t+h

Worked solution

Differentiate the specified function and substitute only after differentiating.
Apply the stated relation and retain its conditions.
$f'(20)=\lim_{h\to0}(40+h)=40$
Cancel h only while h≠0, then take the limit.

The requested value is 40.

Checks and common pitfalls: Cancel h only while h≠0, then take the limit.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment