Answer: (u′v − uv′)/v².
- A (u′v − uv′)/v²
- B (u′v + uv′)/v²
- C u′/v′
- D just uv′
Correct answer: A. (u′v − uv′)/v²
Explanation: The quotient rule gives (u/v)′ = (u′v − uv′)/v².
f(x)=|x| is perfectly continuous at x=0 (no break, no jump), but the curve has a sharp corner there: approaching from the left gives slope -1 and from the right gives slope +1 - since these one-sided derivatives disagree, the function is not differentiable at that point.
Concept context
When a function has no breaks (continuity) and when it has a well-defined slope (differentiability), plus rules for differentiating implicit, inverse trig, exponential, log, and parametric functions.