The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

partial differentiate 1/|x-y|with respect to x

Partial differentiate 1/|x-y|with respect to x where x and y are both vectors. The answer is - (x-y)/|x-y|^3. Not sure why though.
Reply 1
Avatar for ztibor
ztibor
10
Original post by noisy06
Partial differentiate 1/|x-y|with respect to x where x and y are both vectors. The answer is - (x-y)/|x-y|^3. Not sure why though.


The partial derivative is a vector so you have to multiply the derivative by
x⃗−y⃗∣x⃗−y⃗∣\frac{\vec x -\vec y}{|\vec x - \vec y|} unit vector
(edited 11 years ago)
Reply 2
Avatar for noisy06
noisy06
OP
2
Original post by ztibor
The partial derivative is a vector so you have to multiply the derivative by
x⃗−y⃗∣x⃗−y⃗∣\frac{\vec x -\vec y}{|\vec x - \vec y|} unit vector

I see. But what is the derivative exactly? Is it -1/|x-y|^2? It must be because after you multiply it with what you wrote we reach the answer. But I don't understand how we reach -1/|x-y|^2
Reply 3
Avatar for ztibor
ztibor
10
Original post by noisy06
I see. But what is the derivative exactly? Is it -1/|x-y|^2? It must be because after you multiply it with what you wrote we reach the answer. But I don't understand how we reach -1/|x-y|^2


ddr(1r)=ddr(r−1)=(−1)⋅r−2=−1r2\frac{d}{dr}(\frac{1}{r})=\frac{d}{dr}(r^{-1})=(-1)\cdot r^{-2}=-\frac{1}{r^2}
using the rule of
ddx(xn)=n⋅xn−1\frac{d}{dx}(x^n)=n\cdot x^{n-1}
(edited 11 years ago)

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you