Find the Derivative - d/d@VAR f(x)=|x-9|

Problem

d(x−9)/d(x)

Solution

1. Identify the function as a composition of the absolute value function and a linear function.

2. Recall the derivative of the absolute value function |u| which is u/|u| or sgn(u) for u≠0

3. Apply the chain rule by differentiating the outer function |u| with respect to u=x−9 and multiplying by the derivative of the inner function x−9

4. Calculate the derivative of the inner function, which is d(x−9)/d(x)=1

5. Combine the results to find the derivative, noting that it is undefined at x=9

Final Answer

d(x−9)/d(x)=(x−9)/|x−9|

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