39 A level Mathematics Calculus Series Video 22 Part 1

This A-level mathematics calculus video, part of a series, focuses on differentiating exponential functions. We will learn how to differentiate e to the kx and a to the x, understanding the underlying principles and deriving the formulas. The video covers the rule for differentiating e to the kx and provides a step-by-step derivation for differentiating a to the x using the natural logarithm. We begin by exploring the differentiation of e to the kx, where k is a real constant, and discover that its derivative is k times e to the kx. Next, we tackle the differentiation of a to the x, showing that its derivative is the natural logarithm of a multiplied by a to the x. A worked example is included to solidify understanding of these concepts. Visit AxiomTutoring.com and subscribe to @AxiomTutoringCourses.