Math2.org Math Tables: Derivative of b^x

(Math)
(d/dx) bx = bx ln(b)



Proof of (d/dx) bx : from (d/dx) e(x ln b)

Given : (d/dx) ex = ex; Chain Rule; (d/dx) x = 1; (d/dx) (c f(x)) = c (d/dx) f(x).

(d/dx) bx = (d/dx) e(x ln b)
= (d/du) eu (d/dx) (x ln b) (Set u = x ln b)
= e(x ln b) (d/dx) (x ln b) = bx ln(b)