Problem

Find $ dy/dx $ by implicit differentiation. $ …

03:22

Problem 4 Medium Difficulty

(a) Find $ y' $ by implicit differentiation.
(b) Solve the equation explicitly for y and differentiate to get $ y' $ in terms of $ x. $
(c) Check that your solutions to part (a) and (b) are consistent by substituting the expression for $ y $ into your solution for part (a).

$ \frac {2}{x} - \frac {1}{y} = 4 $

Answer

a. $\frac{d y}{d x}=\frac{2 \cdot y^{2}}{x^{2}}$
b. $y^{\prime}=\frac{1}{2(1-2 x)^{2}}$
c. click for solution

More Answers

00:39

Frank L.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Discussion

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Video Transcript

in this trouble were given any question or any question ist over explains why Don't why a seat before you parked anywhere. Stu is implicit differentiation to find Derek Hough. Why Celeste back there with a litter of disrespect, X first time would give us negative two eggs. Great. Uh, second term would give us plus born, uh, scraped. Don't forget, wise. Also functional ex Soviet have divined the eckstrom here, and that is zero since forces From this we see that then the i t x so very little boy would suspect X is equal to two over x described times. Why squared? So that is, too. Once Craig B y squared in Frankie were testifying Function What? Take that. We see that or what? Is he going to over X minus four? From this? We see that. Then why is he going to over X voice for immerse? All right, now let's take their We took that. Why? Prime is an equal to negative one times two over x runs, four for the negative second power times. They were cooked in a function which is made of two over x squared. So the insert is done two over X squared. Well, it's like by two over X words for to the second. Negative second around Now in Percy, where testicle period great is we find our egg and beat. So let's take derivative that we've won. Our baby had to one scraping by spring that import fee we find What? What is right? This is our function boy. So why don't we just plugged it in? If you do so, we see that this is too over x grade multiplied by a widespread where ah Weisberg is too over x once before made one. This is why skirt this. And from this we see that then everything should be direct, scraped, multiplied by two over X minus four to connect a second power and agency. It's the same as what be so. It means that implicit explicit parameters for depreciation give us the same results.

Doruk I.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Top Calculus 1 / AB Educators

Grace H.

Numerade Educator

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Michael J.

Idaho State University