Find the Derivative - d/dx natural log of 3x-1

Problem

d(ln(3*x−1))/d(x)

Solution

1. Identify the outer function as ƒ(u)=ln(u) and the inner function as u=3*x−1

2. Apply the chain rule, which states that d(ln(u))/d(x)=1/u⋅d(u)/d(x)

3. Differentiate the inner function u=3*x−1 with respect to x

d(3*x−1)/d(x)=3

4. Substitute the inner function and its derivative back into the chain rule formula.

d(ln(3*x−1))/d(x)=1/(3*x−1)⋅3

5. Simplify the expression by multiplying the terms.

3/(3*x−1)

Final Answer

d(ln(3*x−1))/d(x)=3/(3*x−1)

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