Answer: -1/sqrt(1-x 2 ).
- A 1/sqrt(1-x<sup>2</sup>)
- B -1/sqrt(1-x<sup>2</sup>)
- C -1/(1+x<sup>2</sup>)
- D 1/(1+x<sup>2</sup>)
Correct answer: B. -1/sqrt(1-x<sup>2</sup>)
Explanation: The derivative of cos inverse x is -1/sqrt(1-x<sup>2</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.