d/dx e^x=e^x
This contant 'e' is troubling me, though it is very interesting.My teacher told that it appears everywhere.
Could you please help me understand it from the basics?

Asked by vicky Sekaran | 2nd Jun, 2015, 09:00: AM

Expert Answer:

fraction numerator d over denominator d x end fraction open parentheses e to the power of x close parentheses equals e to the power of x apostrophe e apostrophe space i s space a space m a t h e m a t i c a l space c o n s tan t space a n d space s tan d s space f o r space E u l e r apostrophe s space n u m b e r. I t space i s space a l s o space k n o w n space a s space N a p i e r apostrophe s space c o n s tan t. I t space i s space a l s o space a n space i r r a t i o n a l space n u m b e r. space e equals 2.171 left parenthesis a p p r o x i m a t e l y right parenthesis B y space d e f i n i t i o n space o f space l i m i t s comma e equals limit as x rightwards arrow infinity of open parentheses 1 plus 1 over x close parentheses to the power of x e to the power of x space s tan d s space f o r space e x p o n e n t i a l space f u n c t i o n. T h e space d e f i n i t i o n space o f e equals sum from n equals 0 to infinity of fraction numerator 1 over denominator n factorial end fraction equals 1 plus 1 over 1 plus fraction numerator 1 over denominator 1.2 end fraction plus fraction numerator 1 over denominator 1.2.3 end fraction plus........ infinity Y o u space c a n space s e a r c h space m o r e space f o r space t h e space r e f e r e n c e s space o f space apostrophe e apostrophe.

Answered by Prasenjit Paul | 2nd Jun, 2015, 12:36: PM

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