1. ## derivative

Find the value(s) of dy/dx for x^2 * y + y^2 = 5 at y =1.

2. What are you having trouble with? Differentiate both sides with respect to x and solve for $y'$. Find the cooresponding x coordinate (since you have y = 1) and plug it in to your expression for $y'$ (it'll contain x's and y's).

3. isn't there something tricky when differentiating y's? tahts what bugs me

4. $x^2y+y^2~=~5$

Tackle this in parts;
Firstly use the product rule.

Let $u=x^2~,~v=y$

$\frac{du}{dx}~=~2x~,~\frac{dv}{dx}~=~\frac{dy}{dx}$

$\frac{d}{dx}(x^2y)~=~x^2\frac{dy}{dx}+2xy$

$\implies~\frac{d}{dx}(x^2y+y^2~=~5)~\implies~x^2\f rac{dy}{dx}+2xy+2y\frac{dy}{dx}~=~0$

$\implies~\frac{dy}{dx}(x^2+2y)~=~-2xy$

$
\implies~\frac{dy}{dx}~=~\frac{-2xy}{x^2+2y}
$

Then substitute your y-value and x-value (which you can calculate using the given formula)

Just like o_O said

5. In case you were wondering i got $-\frac{2}{3}$

6. why can't it be positive 2/3 as well?

7. Originally Posted by DINOCALC09
why can't it be positive 2/3 as well?
It can be i just took x to be positive.