calculate the derivative of |1-x^2|

Question

anonymous · Answer

Have to do it piecewise, but pretty straight forward.

anonymous · Answer

do you think you could show me step by step for each of the two?

anonymous · Answer

Sure. First we break it up piecewise:
$$|a| = b $$$$\implies a = b \text{ if }a \ge 0 \text{ AND } a = -b \text{ if } a < 0$$
Therefore in this case we need to know, when is $1-x^2$ positive, and when is it negative?

anonymous · Answer

Then we can find the derivative will be the derivative of $1-x^2$ on the interval where it's positive, and it will be the derivative of $-(1-x^2) = x^2-1$ on the interval where it's negative. Where it is 0 it will not be differentiable.