Answer: u′v + uv′.
- A u′v + uv′
- B u′v′
- C just uv
- D u′v − uv′
Correct answer: A. u′v + uv′
Explanation: The product rule gives (uv)′ = u′v + uv′.
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.