Exponential Function & Natural Logarithm 指數函數與自然對數

exp(x) = e^x

some coordinates:

(0, 1)
(1, e)

Differentiation 微分 :
d(e^x)/dx = e^x
d(e^ax)/dx = ae^ax


Integration 積分 :

∫ e^x dx = e^x + c
∫ e^ax dx = (1/a)e^ax + c

Maclaurin Series:

e^x = 1 + x + x²/2! + x³/3! + ... + xⁿ/n!

e^a+b = e^ae^b
(e^a)^b = e^ab
e^a+bi = e^ae^bi = e^a(cosb + isinb) = e^acis(b) (Euler's formula)

Inverse of e^x:
ln(x)

natural logarithm 自然對數
log_e(x) = ln(x)

derivative 導數：
d[ln(x)]/dx = 1/x

Exponential Function plotted by Matlab:

相關資料

Exponential Function (Wikipedia)
Matlab: Draw an Exponential Function with exp() with a custom Y-axis at x = 0