Find the Derivative - d/dx natural log of 10x

Problem

d(ln(10*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 which states that d(ln(u))/d(x)=1/u⋅d(u)/d(x) where u=10*x

3. Differentiate the inner function u=10*x with respect to x which gives (d(10)*x)/d(x)=10

4. Substitute these values into the chain rule formula to get 1/(10*x)⋅10

5. Simplify the expression by canceling the constant factor 10 from the numerator and denominator.

Final Answer

d(ln(10*x))/d(x)=1/x

Want more problems? Check here!