Answer: 2e 2x.
- A 2e<sup>2x</sup>
- B e<sup>2x</sup>
- C 2x·e<sup>2x</sup>
- D e<sup>2x</sup>/2
Correct answer: A. 2e<sup>2x</sup>
Explanation: By the chain rule, dy/dx = e<sup>2x</sup>·2 = 2e<sup>2x</sup>.
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.