How do you find the derivative of #abs(x-1)#?

Answer 1

#-1# for #x<1#, #+1# for #x>1# and undefined at #x=1# as the two one-sided limits of #x+h# as #h to 0# are different depending on whether #h>0# or #h<0#.

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Answer 2

To find the derivative of abs(x-1), you can use the definition of the absolute value function and apply the rules of differentiation. The derivative of abs(x-1) is given by:

d/dx [abs(x-1)] = (x-1) / abs(x-1)

However, if x = 1, the absolute value function is not differentiable. So, the derivative exists for all x ≠ 1.

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Answer from HIX Tutor

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.

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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