# Thread: Could anyone help me with the steps to solve this differentiation problem?

1. ## Could anyone help me with the steps to solve this differentiation problem?

Could anyone be so kind to help me with this problem, with step by step explanations!

Thank you

2. ## Re: Could anyone help me with the steps to solve this differentiation problem?

1. $E_N = -Ar^{-1} + Br^{-n}$

$\dfrac{dE_N}{dr} = Ar^{-2} - n \cdot Br^{-(n+1)} = \dfrac{A}{r^2} - \dfrac{n \cdot B}{r^{n+1}}$

$\dfrac{dE_N}{dr} = 0 \implies \dfrac{A}{r^2} = \dfrac{n \cdot B}{r^{n+1}}$

2. since $r > 0$ ...

$A = \dfrac{n \cdot B}{r^{n-1}} \implies r^{n-1} = \dfrac{n \cdot B}{A}$

$r_0 = \left(\dfrac{n \cdot B}{A}\right)^{\frac{1}{n-1}}$

I'll let you complete part 3 on your own ...