For STEM students

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You have been stuck on question four for forty minutes. The answer in the back is 2x·cos(x²), yours is not, and nothing in the worked example tells you which line broke.

LearnFastAI reads your working and tells you exactly which line broke, and which rule you missed on it — then asks you the one question that gets you unstuck.

It stops short of writing the final answer for you. That part is yours.

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Calculus I · Problem 4differentiate
  1. 1f(x) = \sin(x^2)
  2. 2\text{let } u = x^2 \quad\Rightarrow\quad f = \sin(u)
  3. 3\frac{df}{dx} = \cos(u)
  4. 4\frac{df}{dx} = \cos(x^2)

You differentiated sin(u) but stopped there. What does the chain rule say you still owe?

first mistake

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Snip your working. LearnFastAI finds the first line that breaks and names the rule you missed.

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Snip a single line from a worked example and get the justification for why it holds.

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A solver knows the answer. It does not know your page.

Type a problem into a solver and you get a final number. It tells you nothing about the four lines you actually wrote, so you still do not know where you went wrong — and in the exam hall you find out you never learned the step you were missing.

LearnFastAI works on your working. It names the line, names the rule, and leaves the last step to you — which is also why it is the kind of tool your course is likely to allow.

A solver says

f′(x) = 2x·cos(x²)

You learn nothing about why yours was wrong.

LearnFastAI says

Line 3 differentiates sin(u) but never accounts for u changing with x.

You find the chain rule yourself, and remember it.

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Real problems, real corrections

These are genuine responses. Pick a problem and a mode.

Your working

Find ddx[sin⁡(x2)]\frac{d}{dx} \left[ \sin(x^2) \right].
Problem: Find ddx[sin⁡(x2)]\frac{d}{dx} [\sin(x^2)] Step 1: Let f(u)=sin⁡(u)f(u) = \sin(u), where u=x2u = x^2. Step 2: ddu[sin⁡(u)]=cos⁡(u)\frac{d}{du} [\sin(u)] = \cos(u) Step 3: Therefore, ddx[sin⁡(x2)]=cos⁡(x2)\frac{d}{dx} [\sin(x^2)] = \cos(x^2) <-- Student finished here

Step 3: ddx[sin⁡(x2)]=cos⁡(x2)\frac{d}{dx} [\sin(x^2)] = \cos(x^2)

Omitted Inner Derivative (Chain Rule)

When differentiating a composite function f(g(x))f(g(x)), you must multiply the derivative of the outer function f′(g(x))f'(g(x)) by the derivative of the inner function g′(x)g'(x).

Hint

What is the derivative of the inner term u=x2u = x^2 with respect to xx?

The rule

\frac{d}{dx}[f(g(x))] = f'(g(x)) \cdot g'(x)

Calculus I · Chain Rule with Composite Polynomials

Before the exam

Your mistakes become a revision list

Every correction is filed by the skill it belongs to. After a few weeks you stop guessing what to revise.

Chain rule on composite functions

Calculus I

×7repeating

Sign convention in kinematics

Mechanics

×4improving

Integration by parts, second term

Calculus II

×3repeating

Row operations on augmented matrices

Linear Algebra

×1new

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Questions

Reasonable objections

It is designed as a checker, not an answer generator. In Check and Hint modes the model is instructed to identify the first broken line and offer a next-step hint without completing the problem. AI can still make mistakes, so treat the response as tutoring guidance and keep doing the work yourself.

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The browser checker works. The overlay is the one you will still be using in week nine: three keys over your own notes, no tab switching, nothing re-typed.

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