Order the steps of differentiating $y = \sin(3x^{2} + 1)$ by the chain rule.

1. Identify the outer function sine and the inner function 3 x squared + 1
2. Differentiate the outer function, leaving the inner alone, to get cos(3 x squared + 1)
3. Differentiate the inner function to get 6x
4. Multiply the two results to get 6x cos(3 x squared + 1)

Step 1 is the step people skip, and skipping it is why step 3 gets forgotten. The final answer keeps the inner expression intact inside the cosine and multiplies by its derivative outside, omit that factor and the answer is wrong by exactly 6x.