From the course: Complete Guide to Calculus Foundations for Data Science
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Logarithmic derivatives
From the course: Complete Guide to Calculus Foundations for Data Science
Logarithmic derivatives
- [Instructor] Now let's explore logarithmic derivatives. These are derivatives that contain logarithms of variables or functions within the logarithms. You will notice how these derivatives function similarly to those of exponents, which makes sense with how they are related to each other. Let's begin by looking at general logarithmic functions in the format, f of x equals log base a of x where x is greater than zero, a is greater than zero, and a is not equal to one. Note that a is some sort of a real number here. As I mentioned previously, you cannot use any of the previous rules to solve this type of function because the variable is within a logarithm. If you wish to get the derivative of a function f of x equals log base a of x, it will then be in the format of f prime of x equals one divided by the natural log of a multiplied by x. Note that the natural log of a multiplied by x is all in the denominator of that fraction. Essentially, this will simplify your derivative to be the…
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