Implicit Derivative of this Function

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[Solved]Implicit Derivative of this Function

1. The problem statement, all variables and given/known data

Find the implicit Derivative of this function:
1/x+1/y=1

2. Relevant equations
Chain Rule, Quotient Rule ... ?


3. The attempt at a solution

1/x-(y'/y^2)=1
(y'/y^2)=1-1/x
y'=1/y^2-y^2/x

The answer seems to be (-y^2/x^2). I have no idea how that happened. Any help would be most appreciated....
 
Last edited:
42
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It doesn't look like u took the derivative of the (1/x) from the work provided
 
42
0
Also you may want to try to rewrite your function as x^(-1)+y^(-1)=1
 
My new work goes something like

-1/x^2+y'/y^2=1
y'/y^2=1-1/x^2

y' = y^2((x^2+1)/x^2)
y' = y^2-y^2/x^2


Uh.... Could you tell me what I'm doing wrong (Ie, is this an algebra mistake or is my calc itself off)? Again, any help is appreciated...
Forgot to realize the derivative of 1 is zero.... sorry....
 
Last edited:

HallsofIvy

Science Advisor
41,620
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My new work goes something like

-1/x^2+y'/y^2=1
You original function was given by 1/x+ 1/y= 1
You should have a "-" on both x and y and the derivative of 1 is 0.

y'/y^2=1-1/x^2

y' = y^2((x^2+1)/x^2)
y' = y^2-y^2/x^2


Uh.... Could you tell me what I'm doing wrong (Ie, is this an algebra mistake or is my calc itself off)? Again, any help is appreciated...
Forgot to realize the derivative of 1 is zero.... sorry....
 

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