Differentiation rules

Rather than computing the limit definition every time, differentiation rules give shortcuts: the power rule says the derivative of x^n is n times x^(n-1), and the chain rule handles composite functions. For (2x + 1)^3, the chain rule gives 3(2x + 1)^2 times 2 = 6(2x + 1)^2, which checks out against expanding (2x+1)^3 = 8x^3 + 12x^2 + 6x + 1 and differentiating term by term to get 24x^2 + 24x + 6, the same result.

This explanation is AI-generated and can occasionally be wrong.

Vibistic AI

🔒 We never store your messages. The free built-in AI runs through Vibistic's own server, on Cloudflare's own AI infrastructure. You can also add your own API key to send messages straight from your browser to your AI provider instead.

Ask a question about Differentiation rules, like "can you give me another example?"

Your notes

Test your knowledge

This test is AI-generated and can occasionally be wrong. If something looks off, use Report below.

No API key configured yet. Clicking below will ask whether to add one or take a free version of this test when one is available.