LetA be an n X n matrix. Prove that the columns of A span R n if and only if the rows of A are linearly independent.
Exponential Functions: 8.1 Differentiation and Integration Copyright © Cengage Learning. All rights reserved. Differentiation of Exponential Functions The natural base e is the most convenient base for exponential functions. One reason for this claim is that the natural exponential function f(x) = e is its own derivative. 2 Differentiation of Exponential Functions Note: You can interpret this result geometrically by saying that the slope of the graph of f(x) = e at any point (x, e ) is equal to the y-coordinate of the point, as shown in Figure 8.1. Figure 8.1 3 Example 1 – Differentiatin