Learn derivatives with an AI tutor that shows every step

A derivative measures how fast something changes. Most students can recite the power rule but lose marks on chain-rule composites and quotient signs. Noeta finds which of those specific steps you miss, then brings it back days later so it actually sticks.

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What this covers

Limits definition of the derivative
Power, product, and quotient rules
Chain rule and composite functions
Implicit and logarithmic differentiation
Tangent lines, rates of change, optimisation

Worked example

Problem

Differentiate f(x) = (3x² + 1)⁵

1
Spot the structure
This is a composite: an outer power u⁵ with inner u = 3x² + 1, so the chain rule applies.
2
Differentiate the outer function
d/du (u⁵) = 5u⁴, which gives 5(3x² + 1)⁴.
3
Differentiate the inner function
d/dx (3x² + 1) = 6x.
4
Multiply the two
f′(x) = 5(3x² + 1)⁴ · 6x.

Answer: f′(x) = 30x(3x² + 1)⁴

Mistakes that cost marks

Applying the power rule to the whole bracket and forgetting the inner derivative.
Dropping the minus sign in the quotient rule numerator.
Treating a product as if derivatives multiply: (fg)′ ≠ f′g′.

Questions students ask

What is the fastest way to learn derivatives?

Practise one rule at a time with full worked steps, then mix rules in random order. Noeta schedules that mixing automatically using spaced repetition.

Can Noeta check my derivative homework?

Yes — photograph the problem and Noeta returns the reasoning step by step, not just the final answer.

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