Derivation of the electric field from the potential

AI Thread Summary
The discussion revolves around calculating the electric potential (V) and electric field (Ex) for an electric dipole consisting of two equal and opposite charges separated by a distance. The user has successfully derived the expression for V but is struggling to derive Ex from V using the quotient rule. The provided expression for Ex is derived by taking the negative derivative of V with respect to x. The key suggestion is to apply the quotient rule for differentiation to arrive at the correct formula for Ex, which involves manipulating the terms in the expression for V. Additionally, there is a reminder to avoid posting the same question across multiple forums to maintain clarity in discussions.
stargirl22
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I am studying for a test and i can't figure out for the life of me how my book derived the solution for this problem I know it has to be basic i just don't see it...

An electric dipole consists of two charges of equal magnitude and opposite sign separated by a distance 2a... The dipole is along the x-axis and is centered at the origin.
calculate V and Ex if point P is located anywhere between the two charges.

I understand the concept of this, and have calculated V, which is [ (2*(Ke)*q*x) / ((a^2) - (x^2)) ] and i know how to start the problem of Ex...

Ex = - (dV/dx) = - [ (2*(Ke)*q*x) / ( (a^2) - (x^2) ) ...

But I can't remember or figure out for the life of me how they got

= - 2*(Ke)*q * [ { (a^2) + (x^2) } / { ( (a^2)-(x^2) )^2 } ]

Can Anyone please help? :D
 
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try using the quotient rule for the derivation! You will get it!
 
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