Find the Derivative - d/dx natural log of x/4

Problem

d(ln(x/4))/d(x)

Solution

1. Identify the function as a composition of the natural logarithm and a linear function, which requires the use of the chain rule.

2. Apply the chain rule by taking the derivative of the outer function, ln(u) which is 1/u and multiplying it by the derivative of the inner function, x/4

3. Differentiate the inner function x/4 with respect to x which results in 1/4

4. Substitute the inner function back into the derivative of the outer function to get 1/(x/4)⋅1/4

5. Simplify the expression by multiplying the terms.

Final Answer

d(ln(x/4))/d(x)=1/x

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