Find the Derivative - d/dx |x-4|

Problem

d(x−4)/d(x)

Solution

1. Identify the function as a composition involving the absolute value function |u| where u=x−4

2. Recall the derivative of the absolute value function |u| with respect to u is u/|u| or |u|/u for u≠0

3. Apply the chain rule by multiplying the derivative of the outer function by the derivative of the inner function x−4

4. Calculate the derivative of the inner function, which is d(x−4)/d(x)=1

5. Combine the results to find the derivative for x≠4

Final Answer

d(x−4)/d(x)=(x−4)/|x−4|

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