Find the Derivative - d/dx natural log of 7x

Problem

d(ln(7*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. Substitute u=7*x into the formula.

4. Differentiate the inner function 7*x with respect to x which results in 7

5. Multiply the results together.

d(ln(7*x))/d(x)=1/(7*x)⋅7

6. Simplify the expression by canceling the common factor of 7 in the numerator and denominator.

7/(7*x)=1/x

Final Answer

d(ln(7*x))/d(x)=1/x

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