Differentiation

Practise limit-definition questions, core derivative rules, and composite functions.

Focus points

✓Use the limit definition with confidence.

✓Apply the power rule and product structures accurately.

✓Spot where chain rule thinking is needed.

Orin

The Wise Owl

Guides study flow, revision planning, and calmer focus sessions.

Practice set

Question lineup

Mark each one done as you go — finish them all to claim your chips.

6 revision prompts

Question 1OpenStax Calculus Volume 1, Ch. 3 Review Exercises, 371

Use the limit definition of the derivative for f (x) = \sqrt{x + 4} .

Question 2OpenStax Calculus Volume 1, Ch. 3 Review Exercises, 372

Use the limit definition of the derivative for f (x) = \frac{3}{x} .

Question 3OpenStax Calculus Volume 1, Ch. 3 Review Exercises, 373

Find the derivative of f (x) = 3 x^{3} - \frac{4}{x^{2}} .

Question 4OpenStax Calculus Volume 1, Ch. 3 Review Exercises, 374

Find the derivative of f (x) = {(4 - x^{2})}^{3} .

Question 5OpenStax Calculus Volume 1, Ch. 3 Review Exercises, 391

Differentiate f (x) = x^{3} (2 x + 5) .

Question 6OpenStax Calculus Volume 1, Ch. 3 Review Exercises, 399

Differentiate y = \sqrt{1 + x^{2}} .