Hi normalguy,
It all depends on how you define those functions.
So, what is your definition of ? How about ?
I need short, sweet, simple proofs for all the derivatives of , , and concurrently so as to avoid a "chicken or the egg" situation in which 1 proof relies on one of the other 3 results.
Note:
Caution: Do not commit circular reasoning like what I have encountered.
Anyone who can do so is likely to benefit most of us who are learning derivatives.
"Proof is what sets mathematics apart from every other science." ----Prove It, MHF Contributor
Thank You.
if you accept the fact that , then ...
that equation is not what I posted ... if you want what you call "a non-circular proof", then you need the necessary background information to understand the proof.
e (mathematical constant) - Wikipedia, the free encyclopedia
I got it. 1/xlna
so you are using d/dx(lnx)=1/x to proof the derivative of
But I am curious to know which was proven first? derivative of or ?
My textbook says in the special case where a=e for , the derivative is 1/xlne=1/x. Hence I assume derivative of should be proven first!
But your working seems to suggest otherwise.
That is correct is read correctly.
You really do need to learn to use symbols.
Why not learn to post in symbols? You can use LaTeX tags
[tex]y=\log_a(x)~\Rightarrow y'=\dfrac{1}{x\ln(a)}[/tex] gives
Not being able to read your post slows us down.
Hello, normalguy!
Do you really want four separate proofs?
That is a lot of unnecessary work.
If you insist on four proofs, I suggest you find them yourself.
. .
. .
. .
. .
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I'll prove the first one . . . The others will follow nicely.
We have: .
. . . . . . . . . . . . .
. . . . .