Find the Derivative - d/dx natural log of 14x

Problem

d(ln(14*x))/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 for the natural logarithm, which states that d(ln(u))/d(x)=1/u⋅d(u)/d(x)

3. Set u=14*x which means d(u)/d(x)=14

4. Substitute these values into the chain rule formula.

d(ln(14*x))/d(x)=1/(14*x)⋅14

5. Simplify the expression by canceling the constant factor of 14 from the numerator and the denominator.

14/(14*x)=1/x

Final Answer

d(ln(14*x))/d(x)=1/x

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