Answer: e x.
- A x e<sup>x-1</sup>
- B e<sup>x</sup>
- C x e<sup>x</sup>
- D e
Correct answer: B. e<sup>x</sup>
Explanation: The exponential function e<sup>x</sup> is its own derivative.
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.