# Recent content by FilupSmith

1. ### Can you derive e^x by first principles?

Awesome. Thanks! This is so interesting!
2. ### Can you derive e^x by first principles?

Thank you guys. Your explanations were all very informative!
3. ### Help with Einstein and Planck's Views Question

I will. Thank you ~| FilupSmith |~
4. ### Help with Einstein and Planck's Views Question

Question: Outline how Einstein's and Planck's views of Science differed in relation to Science research being influenced by society an politics. I can't remember anything about this and I'm having trouble finding the information needed. Can some one please help me understand what is is that...
5. ### Horse race:tilting the possibility

Ok. I wasn't sure. Thanks :) ~| FilupSmith |~
6. ### Displacement of a particle

I know what it looks like, I'm just curious about what the displacement would be for non-real x values - but it seems to be that for $x=f\left( t\right)$, x cannot be complex. ~| FilupSmith |~
7. ### Displacement of a particle

Ah, I see. ~| FilupSmith |~
8. ### Displacement of a particle

That sounds most probable. So for the case of $x=\sqrt{t-2}$, $x\in \mathbb{R}$ ? ~| FilupSmith |~
9. ### Displacement of a particle

A few months ago, I stumped my Mathematics teacher with a question when we were learning about displacement of a particle, given a formula. For example, $x=t^{2}-t-1$, where x is in meters and t is in seconds. Anyway, she made it very clear how to solve displacement when given time t...
10. ### Can you derive e^x by first principles?

Thank you very much! And I will be sure to remember that ;) ~| FilupSmith |~
11. ### Can you derive e^x by first principles?

Oh, ok. Thanks :) ~| FilupSmith |~
12. ### Can you derive e^x by first principles?

I am referring to e=2.71828... ~| FilupSmith |~
13. ### LaTeX Question about LaTeX

I looked it up and i believe the only difference is that \tfrac or \frac allow for text sized fractions (great for 1/3, etc.) while \dfrac is best for formulas! Thanks none the less!
Differentiation by first principles is as followed: $$y'=\lim_{h\rightarrow 0}\dfrac {f\left( x+h\right) -f\left( x\right) }{h}$$ So, assuming that $y= e^{x},$ can we prove, using first principle, that: $$\dfrac{dy}{dx}\left( e^{x}\right) =e^x$$ Or is there other methods that are...