Find the Derivative - d/d@VAR f(x) = 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 derivative rule for the natural logarithm, which states d(ln(u))/d(x)=1/u⋅d(u)/d(x)

3. Differentiate the inner function 6*x with respect to x which results in 6

4. Substitute these parts into the chain rule formula to get 1/(6*x)⋅6

5. Simplify the expression by canceling the constant factor 6 from the numerator and denominator.

Final Answer

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

Want more problems? Check here!