Math help

i got x = 2p.

differentiated then solved the two system of equations.

wow, youre a lifesaver dood.

whats your stars ID?

royalsu but i dont play anymore

well u may as well log on and grab the $20 im about to send you

LOL when this is wrong and your prof asks you how you came up with such a stupid answer!

its the right answer imo

how could this possibly be the right answer? plug 2p in for x, and see what you get...

you cannot set the derivatives of both sides equal to each other. that doesn't make sense. graphically, you want to find the intersection of the LH function and the RH function. The derivatives to not have to be equal at this intersection.

uh yes you can, both the derivative and non-derivative have common parts that you can set as equal points. we're not NOT manipulating anything. also how can you even check if its right or wrong? we have p, B, and q constants that we dont even know the value of

actually, plugging it in makes perfect sense. equating Bexp[-2p/p] for both the derivative and non-derivatives gives the same expression

Just gave this a quick glance but I think Gim is right. Differentiating makes no sense. And it seems very strange that the answer does not contain k, q or B.

nvm missread

Could you not answer this just using algebraic manipulation?
edit: didn't work for me because you have to take an even root of a negative number

edit #2: actually looks like that does hold up. you just cant do it the other way (ie integrals)

nope because either side of the equation will always have a log part

pretty sick equation, maybe you need to do laplace or another transformation on this?
otherwise just put it into maple

These aren't solvable in a normal way...

You need a special function called the Lambert function in order to get a solution exactly right, which has the symbol W

If you use Wolfram, then it will tell you:
http://www.wolframalpha.com/input/?i=1/p(B*exp(-x/p))+%3D+(k*q^2)/(x^2)

and the page for the function is here:
http://en.wikipedia.org/wiki/Lambert_W_function

But I haven't used this function before so I don't know how to deal with it completely from writing it out by hand, the examples don't deal with x^2 but I'm sure that this is a step on the right track? Maybe you are supposed to use an approximation or something somewhere, when I first looked at this I tried to write e^x as a series expansion (as 1 + x + (x^2)/2 + (x^3)/3! ... etc) but without some qualifier like x is really small then obviously the series just explodes and isn't useful because the higher terms get really big instead of really small.

Hope this at least gives you some ideas.

jesus christ, im no mathematician

What problem is this for or is it just a standalone maths question?

Because without any context (i.e. assumptions or approximations to make), these are pretty hard and involve the maths stuff above. But with some extra info, it might be simplified in some way.

The Born–Mayer potential included the effect of the repulsive core overlap in the form of an
exponential, so that the net potential between two monovalent ions (as in NaCl) is Coulomb
plus core repulsion, i.e.
E = - k e^2/r+ B exp (-r/p)
*e is charge
*r is the variable, x

1. Use calculus to determine the position of the potential minimum and equate this to
d the observed near neighbour separation. From this to calculate the constant B in
terms of d and other parameters.