Finding the rate of change of x in the equation

tellmesomething
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Homework Statement
##\frac{1}{y} +\frac{1}{x} = \frac{1}{12}##. Find the rate of change of x with respect to time atx=5,y=1, if dy/dt=-1
Relevant Equations
Ok
I rearranged the equation and got
$$12x+12y=xy$$
Differentiating this I get
$$12\frac{dx}{dt} + 12\frac{dy}{dt} = x\frac{dy}{dt} + y\frac{dx}{dt}$$
Substituting the values I get
$$12\frac{dx}{dt} -12= -5+\frac{dx}{dt}$$
SO
$$\frac{dx}{dt}=\frac{7}{11}$$
But if I directly differentiate the given equation
##\frac{1}{y} +\frac{1}{x} = \frac{1}{12}##
I get
$$\frac{-1}{x²} \frac{dx}{dt}-\frac{1}{y²} \frac{dy}{dt}=0$$
And here if I substitute the values I get
dx/dt=25

Im not sure where I went wrong in the first method, I'm guessing the differentiation of d(xy)/dt is a little more complicated. Can someone help me out please?
 
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x=5 and y=1 would imply 1/x + 1/y > 1 > 1/12 … your given point is not on the given curve …

Inconsistent input leads to inconsistent output.
 
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Orodruin said:
x=5 and y=1 would imply 1/x + 1/y > 1 > 1/12 … your given point is not on the given curve …

Inconsistent input leads to inconsistent output.
Okay so if dy/dx doesn't exist then that would mean dy/dt also doesn't? At x=5 and y=1
 
tellmesomething said:
Okay so if dy/dx doesn't exist then that would mean dy/dt also doesn't? At x=5 and y=1
Is this a problem you made up yourself?
 
PeroK said:
Is this a problem you made up yourself?
No it came in isc year 2024
Screenshot_2025-03-02-13-42-19-055_com.whatsapp.jpg
 
What is ISC?
 
PeroK said:
What is ISC?
It's an Indian education board. They certify you with 12th grade diploma if you pass their exam. This is from their mathematics paper last year, and tomorrow I'm taking this same exam, hopefully I won't get absurd questions like these :-( cause under pressure i will not be able to identify what's wrong even.
 
tellmesomething said:
It's an Indian education board. They certify you with 12th grade diploma if you pass their exam. This is from their mathematics paper last year, and tomorrow I'm taking this same exam, hopefully I won't get absurd questions like these :-( cause under pressure i will not be able to identify what's wrong even.
Sadly, it seems, there are a lot of flawed questions in exam papers these days. You can see how someone who doesn't really understand what they are doing could construct a problem like this. It never occurs to them that the first equation in ##x## and ##y## must be satisfied by the point they specify.
 
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PeroK said:
Sadly, it seems, there are a lot of flawed questions in exam papers these days. You can see how someone who doesn't really understand what they are doing could construct a problem like this. It never occurs to them that the first equation in ##x## and ##y## must be satisfied by the point they specify.
It is what happens when someone takes last year’s exam question and change the parameters randomly to make a new one …
 
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