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Calculus Physics Programming Chemistry Biology
Ayaan
19 · Engineering Student · Studies alone most evenings
Year 2 3–4 problems stuck per night
I try Gauth, get an answer, copy the steps, and still do not understand why step three works the way it does. I paste it, move on, and feel like I have not actually learned anything.

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What is the derivative of sin(3x²)?
Use the chain rule: d/dx sin(u) = cos(u) · du/dx. Let u = 3x², so du/dx = 6x. Therefore d/dx sin(3x²) = cos(3x²) · 6x.
I do not get why the chain rule applies here. Can you break it down differently?
Think of it as peeling an onion. The outer layer is sin(·). The inner layer is 3x². You differentiate the outer layer first (keeping the inner as-is), then multiply by the derivative of the inner layer. So: derivative of outer sin(inner) = cos(inner) · derivative(inner).
That makes sense. Can I get a practice problem like this?

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