Question

Find the slope of the tangent line to the curve sqrt(3x+3y)+sqrt(2xy)=11.5 at point (4,5)

Answer 1

I like to do one thing on such a problem that many others do not emphasize. Let's check to see if the point (4,5) is actually ON the curve. Can you do that?

Answer 2

yea 1 sec

Answer 3

11.520708

Answer 4

Close enough? I suppose. Now what? We need a derivative, dy/dx, right?

Answer 5

yes

Answer 6

but idk how to go from here
can you help me this has to be submitted by 11 tonight and i am stuck

Answer 7

This is a nice Chain Rule, Implicit Derivative exercise. Go ahead and tackle the first piece. What do you get?

If y = f(x), then (d/dx)(sqrt(3x+3y)) = ??

Answer 8

This is a implicit derivative.

Answer 9

Excellent. What do you get for that first piece?

Answer 10

im not sure

Answer 11

(1/2)3x+3y^(-1/2)?

Answer 12

1/2[(3x+3y)^-1/2](3+3y')

Answer 13

Kind of. It's pretty hard to read when written like that. You should get:
\[\frac{ 3 + 3(dy/dx) }{ 2\sqrt{3x + 3y} }\]
You may like it better written like this:
\[\frac{ 3 + 3y' }{ 2\sqrt{3x + 3y} }\]
Is that what you managed? I couldn't quite tell.

Answer 14

yea

Answer 15

ohh wait i got the answer! thanks for the help!

Answer 16

That's only one piece. The second chunk requires Chain Rule, Implicit, and Product Rule. Can you get that one?

Answer 17

i mean i was able to find solve the final answer

Answer 18

Alas. It's so much nicer when you share your work. :-)