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(d/dx) b^x = b^x ln(b)


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

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

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


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