Find the Derivative - d/dx y = natural log of 6x

Problem

d(ln(6*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=6*x into the formula.

4. Differentiate the inner function u=6*x with respect to x which results in 6

5. Multiply the results together to get the derivative.

d(ln(6*x))/d(x)=1/(6*x)⋅6

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

6/(6*x)=1/x

Final Answer

d(ln(6*x))/d(x)=1/x

Want more problems? Check here!