Math2.org Math Tables: Derivative of b^x

(Math)

(d/dx)

b^x = b^x ln(b)

Proof of

(d/dx)

b^x : from e^{(x ln b)}

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

b^x = e^{(x ln b)}

= e^u (x ln b) (Set u = x ln b)

= e^{(x ln b)} (x ln b) = b^x ln(b)