Answer: 2x·cos(x²).
- A 2x·cos(x²)
- B cos(x²)
- C 2x·cos x
- D cos(2x)
Correct answer: A. 2x·cos(x²)
Explanation: By the chain rule, dy/dx = cos(x²)·(2x).
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.