2.6 Derivatives of Exponential Functions with Bases Other than e - Analytic Geometry and Calculus I

In this video, we look at the graphs of y=a^x and y=b^x, where a is greater than 1 and where b is between 0 and 1. The first functions are increasing, and the second are decreasing, and both have the derivative natural log of the base, times the original exponential function.
We explore these functions and their derivatives graphically, estimating the derivative values by graphically estimating slopes of tangent lines and checking our result against the corresponding derivative values.
Graph of a^x for a greater than 1: www.desmos.com...
Graph of b^x for 0 less than b which is less than 1: www.desmos.com...