Implicit differentiation

  • #1
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Homework Statement



If [tex] y= \ln \sqrt{xy}[/tex] , find the value of dy/dx when y=1

Homework Equations





The Attempt at a Solution



[tex] \frac{dy}{dx} = \frac{1}{\sqrt{xy}} \cdot \frac{1}{2\sqrt{xy}}\cdot (x\frac{dy}{dx}+y)[/tex]

[tex]\frac{dy}{dx}=\frac{1}{x}[/tex] , when y=1
 

Answers and Replies

  • #2
CompuChip
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Looks correct so far.
Did you try plugging in y = 1 and simplifying?
 
  • #3
HallsofIvy
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You answer should be a number, not a function of x. Since y= ln(xy), when y= 1, 1= ln(x). What is x?
 
  • #4
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You answer should be a number, not a function of x. Since y= ln(xy), when y= 1, 1= ln(x). What is x?

this kept me wondering again , if i differentiate first , then plug y=1 in , i get dy/dx=1/x

and now , if i plug y=1 in first , and differentiate later ,

1= ln sqrt(x)

dy/dx=1/2x

Are they supposed to end up with the same result ?
 
  • #5
rl.bhat
Homework Helper
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In all such problems, you have to differentiate first, then substitute the values.
 

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