Answer: 1/(1+x2).
- A 1/(1+x2)
- B -1/(1+x2)
- C 1/sqrt(1-x2)
- D 1/(1-x2)
Correct answer: A. 1/(1+x2)
Explanation: The derivative of tan inverse x is 1/(1+x2) for all real x.
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.