anonymous
  • anonymous
1/x+1/y=4, and y(5)=5/19. Find y'(5) by implicit differentiation.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Differentiating implicitly w.r.t. x we get: \[-1/(x^2) + -1/(y^2)*(dy/dx)=0\] Rearranging: \[dy/dx = -y^2/x^2\] So dy/dx evaulated at x=5 is -y(5)^2/25 = -1/(19^2) = -1/361
anonymous
  • anonymous
Why isn't it -1/(x^2)+y'/(y^2)=0?
anonymous
  • anonymous
OK differentiating the 1/y term we have: \[(d/dx)1/y = (d/dx)y^{-1} = -1y^{-2}*(dy/dx)\] as I originally posted. Your sign is wrong.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
What I mean is, why aren't you treating y as a function in this case? Or are you notating that by saying it needs to multiply (dy/dx)?
anonymous
  • anonymous
We are treating it as a function; we use the following rule: \[(d/dx)f(y(x)) = (d/dy)f(y)*(dy/dx)\] for an arbitary function f I suggest you read an introductory text to differentiation if you do not understand. this *is* implicit differentiation.

Looking for something else?

Not the answer you are looking for? Search for more explanations.