Review your logarithmic function differentiation skills and use them to solve problems.

How do I differentiate logarithmic functions?

First, you should know the derivatives for the basic logarithmic functions:
start fraction, d, divided by, d, x, end fraction, natural log, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, x, end fraction
start fraction, d, divided by, d, x, end fraction, log, start subscript, b, end subscript, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, natural log, left parenthesis, b, right parenthesis, dot, x, end fraction
Notice that natural log, left parenthesis, x, right parenthesis, equals, log, start subscript, e, end subscript, left parenthesis, x, right parenthesis is a specific case of the general form log, start subscript, b, end subscript, left parenthesis, x, right parenthesis where b, equals, e. Since natural log, left parenthesis, e, right parenthesis, equals, 1 we obtain the same result.
You can actually use the derivative of natural log, left parenthesis, x, right parenthesis (along with the constant multiple rule) to obtain the general derivative of log, start subscript, b, end subscript, left parenthesis, x, right parenthesis.
Want to learn more about differentiating logarithmic functions? Check out this video.

Practice set 1: argument is x

Problem 1.1
h, left parenthesis, x, right parenthesis, equals, 7, natural log, left parenthesis, x, right parenthesis
h, prime, left parenthesis, x, right parenthesis, equals, question mark
Please choose from one of the following options.

Want to try more problems like this? Check out this exercise.

Practice set 2: argument is a polynomial

Problem 2.1
g, left parenthesis, x, right parenthesis, equals, natural log, left parenthesis, 2, x, start superscript, 3, end superscript, plus, 1, right parenthesis
g, prime, left parenthesis, x, right parenthesis, equals, question mark
Please choose from one of the following options.

Want to try more problems like this? Check out this exercise.