notation check?

[arkanefyre]

Hi, I started taking Calculus this year in HS. I have this assignment which I completed, but I'm not sure if my notations are right. My teacher is OCD about notation, and takes half a mark off each time I use y=f(x), dy/dx, d/dx, etc. wrong. I went over the assignment with a fine-toothed comb, and don't seem to find any mistakes, but coming from a

Comments

[yuhui_luo]

Just on the first page, I'm confused why you answered b) by simply switching around x and y? It seems that that's where you went wrong.

b) is asking for an equation of the form y = f(x), and then you're supposed to just differentiate the question in b) for part c) instead of using implicit differentiation again, and basically supposed to confirm your answer in part a).

So, for b) y = x^3 / (4x^2 - 3) if I'm not mistaken, and then you differentiate that like you normally would.

I haven't looked at the others, but from the first question, it does seem like you have the general hang of implicit differentiation. Just spend a bit more time checking things over, I guess.

[arkanefyre]

Oh! I see my problem. Thank you! I fixed it - I think this is right now?

[rampart]

Lol, some of your d's look like the partial d's, but I doubt your teacher will care about that, unless she's expecting you to work in multi-variate RIGHT NOW.

Most of it looks ok, I think. You have implicit differentiation down pretty well. I think this is one of the topics that never really shows up again in calculus. Much like differentials, newton-rhapson approximations, numerical integration--- etc

[arkanefyre]

Man. That menas I learned implicit for naught? Thanks for taking a look! On the last page, I have yet to take out the dy/dx - is that acceptable for an answer?

[rampart]

The third line in the last page looks like dy/0x...

Anyway, I think it depends on how strictly your teacher wants you to carry out all the calculations. Is there anyway to shoot an e-mail over and ask?

[arkanefyre]

She usually wants us to solve for dy/dx. In this case, I have no clue how. Unless it becomes 2x-y/2xy-4?

[korean_guy_01]

On #3 in line 3 you don't have the end bracket for where you need to distribute the minus sign.

[arkanefyre]

I can't believe I missed that! Thanks for pointing it out!