Find the Derivative - d/dx y = log of 3x

Problem

d()/d(x)*ln(3*x)

Solution

1. Identify the function as a natural logarithm of a composite function, where y=ln(u) and u=3*x

2. Apply the chain rule for the derivative of a natural logarithm, which states d(ln(u))/d(x)=1/u⋅d(u)/d(x)

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

4. Substitute the values into the chain rule formula to get 1/(3*x)⋅3

5. Simplify the expression by canceling the common factor of 3 in the numerator and denominator.

Final Answer

d(ln(3*x))/d(x)=1/x

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