Problem

(a) Find $ y' $ by implicit differentiation. (b)…

02:22

Problem 3 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).

$ \sqrt{x} + \sqrt{y} = 1 $

Answer

a. $y^{\prime}=-\frac{\sqrt{y}}{\sqrt{x}}$
b, $y^{\prime}=-\frac{1}{\sqrt{x}}+1$
c. From part $(\mathrm{a}), y^{\prime}=-\frac{\sqrt{y}}{\sqrt{x}}=-\frac{1-\sqrt{x}}{\sqrt{x}} \quad[\text { from part }(\mathrm{b})]=-\frac{1}{\sqrt{x}}+1,$ which agrees with part

More Answers

01:38

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 problem with unit in question or any question of spirit of explosive period of Isaac will impart every excuse, implicit differentiation to find very why. So I stood out. Let's take there with all the time. First I would give us one over to skirt ex wife's second term with us one over to skirt off. Why now? They were taught here function since why is also s o. B have ideas, and that is zero because one, it's just constant. So let's leave you I d x one side you have. Do you mind? The X is, um, equal to negative one board to start it affects the like. Buy one over to skirt these twos. Cancel out from unifying. The answer is negative Stories of flying white bastard Ex party were asked you explicit, sold for war and then take Geritol function. So we see that spirit of what it is you could warn minus skirt X. Now, if you take skirt off science, we find why to be one minor skirt of X. It's great. Now let's find Eric joke. That's quite plain. Is anything to two times or minus scared little X time. Stay with inter function, which is negative. One or two discovered X twos will cancel out when we find them. The answer to be negative. Short skirt of likes running for your life by sparing root ex All right, now in currency were testicle parents be there were two refund and a and A B. So let's take the other two off the function. Why that be finding it. So we have negative conspirator. Why the white spirit? Thanks In part TV, find what our function what is from this? We see that y is equal to so negative skirt boots off one, um minus skirted off X squared Screwed your wife five Spirit X distributed and spare will cancel out. I'm a wind up with negative off one minus skirted X divided by spirit of X and that is he going to discourage it off X minus storm like spirit that bites as you can see This same less what? Okay, so we can see that you guys say that both implicit explicit depreciation gave us the same result

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

Catherine R.

Missouri State University

Heather Z.

Oregon State University

Caleb E.

Baylor University

Michael J.

Idaho State University