partial differentiation with log function. Can someone please help as I am stuck, I need to show that phi=k/(2 pi)log(x^(2)+y^(2))^(1/2) satisfies Laplaces equation, however I cannot seem to differentiate this function.

Kelton Bailey

Kelton Bailey

Answered question

2022-09-03

Partial differentiation with log function.
Can someone please help as I am stuck,
I need to show that
ϕ = k 2 π log ( x 2 + y 2 ) 1 / 2
satisfies Laplaces equation, however I cannot seem to differentiate this function. Note k is a constant.
How do I go about partially differentiating
log ( x 2 + y 2 )
I was thinking, using chain rule, just call
x 2 + y 2 = r
so
1 r log r + log r
Any help is appreciated.

Answer & Explanation

Cullen Kelly

Cullen Kelly

Beginner2022-09-04Added 7 answers

I would think that you would immediately use l o g ( x 2 + y 2 ) = 1 2 l o g ( x 2 + y 2 ). That will simplify your problem.

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