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#1 2005-12-01 12:57:07

mikau
Member
Registered: 2005-08-22
Posts: 1,504

multiple differentials

one thing thats bothering me. Sometimes it seems the rules for differentiating are not always true. For instance:

e^2

we know the differential of e^x = e^x dx so the slope of the line at 2 is e^2

But what if we used the fact that the derivative of x^n = nx^(n-1) ?

by this definition the derivative of e^2 should be ne^1 or 2e^1 but this is different then e^2!

So what if you took the derivitive of n^2 and n just happens to equal e or close to it? Would the derivative be wrong?

This is disturbing.


A logarithm is just a misspelled algorithm.

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#2 2005-12-01 13:23:39

irspow
Member
Registered: 2005-11-24
Posts: 455

Re: multiple differentials

I think that you are just a little bit confused on this one.  The derivative of e^x is e^x, but that is because you are differentiating a variable exponent.  There are a lot of derivatives associated with logarithmic and exponential functions.

     The derivative of e^2 would be 2e because the exponent was a constant and you could use the x^n = nx^(n-1) rule.  This rule is used when a variable is raised to a constant power. Play close attention to what the variable is in the equation.  Look around the internet for rules for differentiation of logarithmic functions and you will see where you went wrong.

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#3 2005-12-01 13:51:42

darthradius
Member
Registered: 2005-11-28
Posts: 97

Re: multiple differentials

irspow wrote:

The derivative of e^2 would be 2e because the exponent was a constant and you could use the x^n = nx^(n-1) rule.

eh?

e²  is a constant, and so d/dx would just be zero...


The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
                                                             -Bertrand Russell

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#4 2005-12-01 14:40:06

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: multiple differentials

[Sh]e's right! Technically we should say the slope of e^x when x equals two.

I think I see where the confusion is now, irspow, thanks.


A logarithm is just a misspelled algorithm.

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#5 2005-12-02 04:34:31

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: multiple differentials

Or we could say that we were finding d/de.


Why did the vector cross the road?
It wanted to be normal.

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