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

Problem

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

Solution

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

2. Apply the Chain Rule which states that d(ln(u))/d(x)=1/u⋅d(u)/d(x) where u=7*x

3. Differentiate the inner function u=7*x with respect to x which gives (d(7)*x)/d(x)=7

4. Substitute these values into the Chain Rule formula to get 1/(7*x)⋅7

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

Final Answer

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

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