Find the Derivative - d/dx log of 5x

Problem

d((log_)(5*x))/d(x)

Solution

1. Identify the function as a common logarithm, which is assumed to be base 10, written as (log_10)(5*x)

2. Apply the change of base formula to rewrite the logarithm in terms of the natural logarithm: (log_10)(5*x)=ln(5*x)/ln(10)

3. Apply the constant multiple rule to move the constant factor 1/ln(10) outside the derivative.

4. Apply the chain rule to differentiate ln(5*x) which results in 1/(5*x)⋅(d(5)*x)/d(x)

5. Differentiate the inner function 5*x to get 5

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

Final Answer

d((log_)(5*x))/d(x)=1/(x*ln(10))

Want more problems? Check here!