# What is the derivative of #|x|#?

In general, there is no derivative as

However, some may find it useful to find the derivative of the function by breaking it into pieces and kind of "avoiding" the discontinuity.

Finding the derivative of the function by dissecting it and essentially "avoiding" the discontinuity, however, might be helpful to some people.

The derivative is 1 because the positive side of the function is just a line with a positive slope of 1.

The derivative is -1 when looking at the function's negative side, which is just a line with a negative slope of 1.

Since the two one-side limits conflict at zero, there is obviously a discontinuity and no derivative can be defined.

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The derivative of |x| is not defined at x = 0. For x > 0, the derivative is 1, and for x < 0, the derivative is -1.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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