Please prove the monotonicity of exponential function Proof Halo, what is derivative? Is there another way?

Please prove the monotonicity of exponential function Proof Halo, what is derivative? Is there another way?

The exponential function f (x) = a ^ x, a > 0, and a! = 1. (Note: the requirement of the exponential function for the base number, otherwise it is not an exponential function,! = is not equal to the sign). The derivation of F '(x) = a ^ x ln a, because a ^ x > 0 is always true, so there are: when 0 < a < 1, ln a < 0, f' (x) < 0, the

If f (x) = (A-3) (A-2) x is an exponential function, find the value of F (3)

Is f (x) = (A-3) (A-2) x an exponential function?

Given that the function f (x) = loga1 mxx + 1 (A & gt; 0, a ≠ 1, m ≠ - 1), is an odd function defined on (- 1,1). (I) find the value of F (0) and the value of real number m; (II) judge the monotonicity of function f (x) on (- 1,1) when m = 1, and give the proof; (III) if f (12) & gt; 0 and f (b-2) + F (2b-2) & gt; 0, find the value range of real number B

(1) ∵ f (0) = loga1 = 0. Because f (x) is an odd function, f (- x) = - f (x) {f (- x) + F (x) = 0 ∵ log a & nbsp; MX + 1-x + 1 + log a 1-mxx + 1 = 0; ∵ log a & nbsp; MX + 1-x + 1 · 1-mxx + 1 = 0 {MX + 1-x + 1 · 1-mxx + 1 = 1, that is ∵ 1-mx2 = 1-x 2 for X in the domain