Later, we defined b 0 = 1, b − n = 1 b n, b 0 = 1, b − n = 1 b n, for a positive integer n, n, and b s / t = ( b t ) s b s / t = ( b t ) s for positive integers s s and t.
![derivative of log base x derivative of log base x](https://amsi.org.au/ESA_Senior_Years/imageSenior/3h_4.png)
In previous courses, the values of exponential functions for all rational numbers were defined-beginning with the definition of b n, b n, where n n is a positive integer-as the product of b b multiplied by itself n n times. The proofs that these assumptions hold are beyond the scope of this course.įirst of all, we begin with the assumption that the function B ( x ) = b x, b > 0, B ( x ) = b x, b > 0, is defined for every real number and is continuous. As we develop these formulas, we need to make certain basic assumptions. Just as when we found the derivatives of other functions, we can find the derivatives of exponential and logarithmic functions using formulas. Logarithmic functions can help rescale large quantities and are particularly helpful for rewriting complicated expressions. As we discussed in Introduction to Functions and Graphs, exponential functions play an important role in modeling population growth and the decay of radioactive materials. In this section, we explore derivatives of exponential and logarithmic functions.
DERIVATIVE OF LOG BASE X HOW TO
So far, we have learned how to differentiate a variety of functions, including trigonometric, inverse, and implicit functions.
![derivative of log base x derivative of log base x](https://i.ytimg.com/vi/fwKVQ0W_91o/maxresdefault.jpg)