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✦Mock · Q 7 of 20

09:12Submit

13 of 20 answered

Differentiate: f(x) = x² sin(x)

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13 answered · 7 remaining · 2 flagged

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Calculus I · 12 sections

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Continue where you left offThe chain rule · Check

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Differentiate: f(x) = (2x² + 1)⁵

There are 3 steps to solve this one.

f is one function wrapped inside another, which is exactly what the chain rule is for. Outside: u⁵. Inside: u = 2x² + 1.

The chain rule differentiates the outside at the inside, then multiplies by the inside's derivative: f′(x) = 5(2x² + 1)⁴ · d/dx(2x² + 1).

The power rule gives d/dx(2x² + 1) = 4x, since a constant has no rate of change. Multiplying the constants leaves 20x(2x² + 1)⁴.

f′(x) = 20x(2x² + 1)⁴

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✓ Saved to your workspace · classified: CalculusTry it: tap any step

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Calculus I · Lecture 12: The chain rule

The rule for differentiating a function that sits inside another one.

Cue columnp.7

Key questionWhen do you need the chain rule?CueDifferentiate the outside, keep the inside, then multiply by the inside derivative. Most misses skip that last step.

Key Terms

Chain rule	d/dx f(g(x)) = f′(g(x)) · g′(x)
Composite function	a function inside another, f(g(x))

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AI study tools FAQ

What are AI study tools?

Software that turns your own course materials, such as slides, handouts, PDFs, and recordings, into the things you actually study from: notes, summaries, flashcards, practice questions, and full mock exams. AceQuiz runs all of them off one uploaded set of materials.

What is the best AI study tool for students?

The best AI study tool is the one that works from your own course materials and then proves the studying worked. Look for four things: it accepts your real files (slides, PDFs, recordings), it generates practice you can take rather than just summaries, it runs a timed mock exam, and it tracks which concepts are weak. AceQuiz was built around all four.

Can AI study tools actually improve exam scores?

The evidence says yes, when they are used for practice testing. The largest meta-analysis of practice testing (Adesope et al., 2017) found students who test themselves outperform students who re-read by about half a standard deviation, which is roughly a 10 percent improvement on a typical class result. Testing with feedback is worth nearly double testing without it (Rowland, 2014). AceQuiz is built around that loop: generate questions from your material, sit a timed mock, then drill the concepts you missed.

Are AceQuiz's AI study tools free?

There's a free tier that doesn't expire: generate quiz questions with no credit card and no trial clock. Paid plans are a simple subscription that unlocks higher limits and advanced features, not a cost per quiz. See our pricing plans for details.

How is AceQuiz different from other AI study tools?

Most tools stop at generating material. AceQuiz measures whether it worked: a timed mock exam built from your course tells you where you stand before exam day, and weak concepts route back into your next practice session automatically.

AI Study Tools
Built for STEM Students

All-in-one AI study tools for every study need