Given the electric potential V= -constant term-*(x^2+R^2)^1/2 - x, I was asked to find the partial derivative of V with respect to X(-dV/dx). I derived -(-constant term- *(x/((x^2+R^2)^1/2))-1) and the homework site said that was wrong. How the heck did I derive that wrong? I don't get it! Help? Excuse me if I don't seem happy. I've been doing this 5-multiple-part-problem homework assignment for the past four, almost five hours and it's frustrated me to the point of being at the verge of tears.

Question

Given the electric potential V= -constant term-*(x^2+R^2)^1/2 - x, I was asked to find the partial derivative of V with respect to X(-dV/dx).  I derived -(-constant term- *(x/((x^2+R^2)^1/2))-1) and the homework site said that was wrong.  How the heck did I derive that wrong?  I don't get it!  Help?  Excuse me if I don't seem happy.  I've been doing this 5-multiple-part-problem homework assignment for the past four, almost five hours and it's frustrated me to the point of being at the verge of tears.

noelgreco · Answer

What did you get?

anonymous · Answer

I got what I said I derived.

noelgreco · Answer

Sorry.  It's a lot easier for these old eyes to read if it's in the equation form.

I get the same derivative as you.

anonymous · Answer

And yet the homework site thinks my derivative is wrong for some reason. *headdesk*

anonymous · Answer

Does your homework site allow you to join all constant to that -constant term- thing, or what.

anonymous · Answer

Lemme use the equation thing to post the equation I was given for electric potential V.
$$V=\frac{ \sigma }{ 2\epsilon _{0} }\sqrt{x ^{2}+R ^{2}}-x$$
The problem wanted -dV/dx

anonymous · Answer

Absolutely nothing wrong w/ your answer. Hmmm....

anonymous · Answer

$$-\frac{ \sigma }{ 2\epsilon_0 }\frac{ x }{ \sqrt{x^2+R^2} }+1$$
right?

anonymous · Answer

Yeah, that's right.  The site calls it a partial derivative with respect to x, but dV/dx should be the same thing since the equation has no y or z in it.

anonymous · Answer

Is there a possibility for the site to wrong? I guess that's why.

anonymous · Answer

That could be.  There was a question on a previous assignment that a teacher proved I did correctly but the site said my answer to was wrong.

anonymous · Answer

Ugh, finally just hit the button to see the answer they wanted.  Their answer was
$$\frac{ \sigma x }{ 2\epsilon _{0} }(\frac{ 1 }{ x}-\frac{ 1 }{ \sqrt{x ^{2}+R ^{2}} })$$
EXACTLY my answer, just left in a weird unsimplified way.  Really, homework site? DX

anonymous · Answer

You did well, that's why no substitute for the real human teacher.

anonymous · Answer

My computer programming teacher is right.  Computers are dumb.

anonymous · Answer

Well, more or less.