## bmelyk Group Title Looking for someone to check my answer: Find an equation of the tangent line through the given point. x 2 y 3 + 15y = 34x, (3, 2) one year ago one year ago

1. bmelyk Group Title

$\frac{ 34-2x }{ 2y+15 }$

2. bmelyk Group Title

thats the answer i got.

3. bmelyk Group Title

well that's what i had for y'

4. asnaseer Group Title

You first need to use implicit differentiation to find an expression for $$\displaystyle\frac{dy}{dx}$$. Then substitute x=3 and y=2 into that expression to get the slope of the tangent line at that point. So then you will know the slope of the tangent line and you also know it passes through the point (3,2) - use this information to calculate the equation of the tangent line.

5. bmelyk Group Title

was my y' equation correct?

6. asnaseer Group Title

it doesn't look correct to me - can you please list your steps so that I can help spot where you may have made a mistake?

7. bmelyk Group Title

$x ^{2}y ^{2}+15y=34x$ $2x*2yy'+15y'=34$ $y'(2y+15)=34-2x$ $y'=\frac{ 34-2x }{ 2y+15 }$

8. asnaseer Group Title

I thought you had $$y^3$$ in the equation listed in your question?

9. bmelyk Group Title

lol so it is.

10. bmelyk Group Title

$y'=\frac{ 34-2x }{ 3y ^{2}+15 }$

11. bmelyk Group Title

did i have it right the second time (right above what you just wrote)

12. asnaseer Group Title

sorry I meant:$\frac{d}{dx}(x^2y^3)=(x^2)\frac{d}{dx}(y^3)+y^3\frac{d}{dx}(x^2)$

13. asnaseer Group Title

you haven't used the chain rule correctly

14. asnaseer Group Title

I mean "product rule"

15. asnaseer Group Title

have a look here: http://www.1728.org/chainrul.htm

16. bmelyk Group Title

$x ^{2}*3y ^{2}y'+y ^{3}2x+15y'=34$

17. asnaseer Group Title

that is correct :)

18. bmelyk Group Title

okay so now i isolate y'

19. asnaseer Group Title

exactly

20. bmelyk Group Title

$y'=\frac{ 34-2xy ^{3} }{ x ^{2}3y ^{2}+15 }$

21. asnaseer Group Title

yup - now follow the other steps that I had listed above.

22. asnaseer Group Title

NOTE: we don't usually write an expression as $$x^23y^2$$ - it is better to write it as $$3x^2y^2$$

23. bmelyk Group Title

ok.

24. asnaseer Group Title

the general rule of thumb is to write in this order: 1. Constants first 2. Then letters in alphabetical order

25. bmelyk Group Title

okay so now i sub in my points right?

26. asnaseer Group Title

correct

27. bmelyk Group Title

so i had: -14/123

28. asnaseer Group Title

perfect! just a couple of more steps to go now :)

29. bmelyk Group Title

is the equation: $y-2=-14/123x+42/123$

30. asnaseer Group Title

yes - that looks correct. I wouldn't have separated the two constants here (the -2 and the 42/123)

31. asnaseer Group Title

you may also want to multiply both sides by 123 to remove the fractions from the final equation.

32. bmelyk Group Title

so how would you make it look?

33. asnaseer Group Title

ok, you got to this equation:$y-2=-14/123x+42/123$first add 2 to both sides to get:$y=-14x/123 + 288/123$then multiply both sides by 123 - what will you get then?

34. bmelyk Group Title

y123=-14x+288

35. asnaseer Group Title

correct - but again, remember to write constants first - so 123y instead of y123

36. bmelyk Group Title

that's not really how you write the equation of a line though.

37. asnaseer Group Title

so I would write the final equation as:$123y=288-14x$

38. asnaseer Group Title

it is still an equation of a line. you can write it in "standard form" as follows:$14x+123y=288$

39. asnaseer Group Title

maybe you are only used to seeing it in the form: $$y=mx +c$$

40. asnaseer Group Title

One last advice before I leave - you wrote one of the terms in your original equation as: -14/123x this can sometimes be confused for: $-\frac{14}{123x}$so it is usually better to write it as: -14x/123