Find the Derivative - d/dx y = natural log of 4x

Problem

d()/d(x)*ln(4*x)

Solution

1. Identify the function as a composition of the natural logarithm and a linear function, requiring 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=4*x into the formula.

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

5. Multiply the components together.

d(ln(4*x))/d(x)=1/(4*x)⋅4

6. Simplify the expression by canceling the common factor of 4 in the numerator and denominator.

4/(4*x)=1/x

Final Answer

d(ln(4*x))/d(x)=1/x

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