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[MATH DERiVATiVE]: Why is d/dx(e^x) = e^x


SiRaLeX
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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?  :P

 

 

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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?  :P

 

Magic.

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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?  :P

 

Do it by definition if it confuses you...  :P

 

definicao+derivada.png

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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.

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  • 1 month later...

Strategst, I know what a derivative is.

 

 

Magic.

Do it by definition if it confuses you...  :P

 

definicao+derivada.png

 

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.  :P

 

 

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