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$5-20$ Find dy/dx by implicit differentiation.$$2 \sqrt{x}+\sqrt{y}=3$$

$\frac{-2 \sqrt{y}}{\sqrt{x}}$

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Differentiation

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you know this problem? We've been given the following curve and we would like to find dy dx by implicit differentiation. The first thing we do want to do here though is rewrite this and so it's right to this. Two X. To the one half. Well it's wider. The one have mm Is equal to three. And then now we can take out a really good from this. The derivative two extra 1/2 Is X. to the negative one half. Why do the one half is 1/2 Either the negative one half. Why prime In the derivative of 30? If we subtract tax and they have one half over. This gives us one half. Why do the name of 1/2? Why prime Is equal to 95? That's the one here. Right? Multiply both sides by two. It's going to get rid of that 1/2 And then divide by Y. to the negative one half. And this gives us why prime is negative two X. The native one half Over wide of the -1 house. Now those negative experiences mean flip where they are in the fraction. And so this tells us why prime does negative to route. Why overruled X.

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