anonymous 3 years ago Find an equation of the tangent line to the curve at the point. x^2+xy+y^2=7 (2,1) please show steps! I need to learn how to do it

1. anonymous

Have you been taught derivatives

2. anonymous

yes, but tomorrow I have an exam on a bunch of stuf and im sooooooo lost!!! I'm just trying to learn it all because I don't understand my professor at all.

3. anonymous

okay lets start with this problem. Every time you take the derivative of a y we need to add y'. Ex) the derivative of 2y^2=6 is 4yy'=0, then you solve for y' We will do the same above. Let's work one term at a time. What is the derivative of x^2?

4. anonymous

2x

5. anonymous

Do implicit differentiation in this one i suppose. do it for both y and x

6. anonymous

thats the prob idk how

7. anonymous

$-{\frac {x+2\,y}{2\,x+y}}$

8. anonymous
9. anonymous
10. anonymous

well when y is dependant variable -(2*x+y)/(x+2*y)

11. anonymous

at 2,1 the slope is -5 -- 4

12. anonymous

I figure it out. But, now I'm stuck on the next problem

13. anonymous

use y=mx+b 1=-5/4*2+b sfb

14. anonymous

b=7/2 so y=-5/4*x+ 7/2 :)

15. anonymous

BTW I graphed it and it works fine both the tangent line and the function yyou gave me do you wanna see it?

16. anonymous

yeah i already figured it out