SiRaLeX Posted May 4, 2016 Share Posted May 4, 2016 d/dx(0.5^x) = -0.693147×0.5^x d/dx(1^x) = 0 d/dx(1.5^x) = 0.405465×1.5^x d/dx(2^x) = 2^x log(2) d/dx(2.71^x) = 0.996949×2.71^x d/dx(e^x) = e^x d/dx(2.72^x) = 1.00063×2.72^x d/dx(3.14^x) = 1.14422×3.14^x d/dx(pi^x) = pi^x log(pi) Explain, anyone? Link to comment Share on other sites More sharing options...
Jacko Posted May 4, 2016 Share Posted May 4, 2016 On 5/4/2016 at 12:08 PM, SiRaLeX said: d/dx(0.5^x) = -0.693147×0.5^x d/dx(1^x) = 0 d/dx(1.5^x) = 0.405465×1.5^x d/dx(2^x) = 2^x log(2) d/dx(2.71^x) = 0.996949×2.71^x d/dx(e^x) = e^x d/dx(2.72^x) = 1.00063×2.72^x d/dx(3.14^x) = 1.14422×3.14^x d/dx(pi^x) = pi^x log(pi) Explain, anyone? Magic. Link to comment Share on other sites More sharing options...
Nyerguds Posted May 4, 2016 Share Posted May 4, 2016 Man, that shit's been ages. You do your homework yourself, lol. Link to comment Share on other sites More sharing options...
GiftS Posted May 7, 2016 Share Posted May 7, 2016 On 5/4/2016 at 12:08 PM, SiRaLeX said: d/dx(0.5^x) = -0.693147×0.5^x d/dx(1^x) = 0 d/dx(1.5^x) = 0.405465×1.5^x d/dx(2^x) = 2^x log(2) d/dx(2.71^x) = 0.996949×2.71^x d/dx(e^x) = e^x d/dx(2.72^x) = 1.00063×2.72^x d/dx(3.14^x) = 1.14422×3.14^x d/dx(pi^x) = pi^x log(pi) Explain, anyone? Do it by definition if it confuses you... Link to comment Share on other sites More sharing options...
Strategst Posted May 12, 2016 Share Posted May 12, 2016 The derivative of a function gives its instantaneous rate of change, or slope, at any given point. The exponential function just so happens to have the same value as its slope at every point. The simplest example is exp^0=1, where the slope of exp^x at x=0 is also 1. Continue inductively from there. Link to comment Share on other sites More sharing options...
SiRaLeX Posted June 15, 2016 Author Share Posted June 15, 2016 Strategst, I know what a derivative is. On 5/4/2016 at 12:29 PM, Jacko said: Magic. Quote Do it by definition if it confuses you... These are the best answers. Except, I'm not sure I can simplify the limit without L'H and knowing that the derivative of e^x is e^x. Link to comment Share on other sites More sharing options...
Plokite_Wolf Posted June 15, 2016 Share Posted June 15, 2016 On 6/15/2016 at 5:39 PM, SiRaLeX said: These are the best answers. Except, I'm not sure I can simplify the limit without L'H and knowing that the derivative of e^x is e^x. There is something called a Google search, which gives the answer (without the L'Hospital rule)... https://www.wyzant.com/resources/lessons/math/calculus/derivative_proofs/e_to_the_x Link to comment Share on other sites More sharing options...
SiRaLeX Posted June 15, 2016 Author Share Posted June 15, 2016 Thank you, Plokite_Wolf! It is all over Google, indeed. But your link is exactly what I was looking for! Link to comment Share on other sites More sharing options...
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