Find the Derivative - d/dx natural log of 2x

Problem

d(ln(2*x))/d(x)

Solution

1. Identify the function as a composition of the natural logarithm ln(u) and the linear function u=2*x

2. Apply the chain rule, which states that d(ln(u))/d(x)=1/u⋅d(u)/d(x)

3. Differentiate the inner function 2*x with respect to x which results in 2

4. Substitute the components into the chain rule formula to get 1/(2*x)⋅2

5. Simplify the expression by canceling the common factor of 2 in the numerator and denominator.

Final Answer

d(ln(2*x))/d(x)=1/x

Want more problems? Check here!