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.

Session plan

Start with the first two questions to warm up before moving into the harder ones.

Use the calculator only after you have set up the working or estimated the answer.

Work through the page like a focused study sheet instead of jumping around.

How to use this page

A cleaner maths workflow

1. Read the prompt carefully

These pages are meant to feel consistent with the rest of the site, but the maths stays front and center.

2. Solve in order

The question list works best as a progression rather than a random set of cards.

3. Use support tools when needed

You can jump back to the calculator or home without losing the overall flow.

Practice set

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}} .