Derivative of e^x from First Principles

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Steps on how to find the derivative of e^x from first principles.

The derivative of e^x is just e^x, this can be proven by finding the derivative of e^x from first principles with the assistance of some index and limit properties.

Music by Adrian von Ziegler

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the tricky part you did not explain ..why lim as x goes to zero of a`x-1/1 = ln a ??

sajidrafique

That doesn't answer the question unless you can show that the limit of (e^h-1)/h is 1 without resorting to l'Hopital's rule or Taylor expansion, both of which require differentiation of the exponential.

JerBoyd

Absolutely nice but background music was mind soothing. So share it

aman-cxlb

You cannot claim this as deriving the derivative of e^x from first principles. At 2:33, you are using the formula derived from this very derivative! This creates a cyclic dependency on proofs.

agytjax

2:14 Where did the limit formula about ln(a) come from?

MurshidIslam

very helpful and straight to the point. No unnecessary info...thanks man

levizwannah

The last bit is circular reasoning. lim (x --> 0) [a^x - 1]/x = ln (a), comes from L' Hopital's rule which you cannot use without knowing that d(a^x)/dx = a^x · ln(a) beforehand. However, if you know that d(a^x)/dx = a^x · ln(a) then there is no reason to prove d(e^x)/dx = e^x from first principles. Just replace a with e in the foregoing differential equation and you have your answer.

johnnolen

where did the limit formula in the top right ( = to ln(a)) come from?

robjows

The soundtrack makes me want to cry watching this!😅😢😅😢😅😢

RichardMaiap

U are using de^x/dx = e^x when u are proofing it

Neo-

What's the real name of background music..??

aythriver

Sounds like it could be part of a Minecraft soundtrack

IonizedComa

Hello
can you please solve this question
f(x)=e^x^2 +1 from First Principles

e +1

zunisuki

Letras y números muy pequeños tuve que quitar el Canal

luisforero

why you no talk?? you can't expect me to understand that

haretztj

The most important step was omitted ( and labeled as "limit formula")...LOL

DGQQ

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