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# implicit differentiation watch

1. Hi guys ,
quick question what would your answer be to the picture i attached you here
Attached Images

2. What exactly are you trying to do?
3. Urhm, what exactly is the question?
4. That expression you wrote down would simplify to .
5. .
It is almost as if the dy's cancel.
6. (Original post by B_9710)
That expression you wrote down would simplify to .
this is the part i don't understand . here's how i do it which gives me the wrong answer : d/dx of y^2 is equal to 2y and 2y. x would give you 2xy . i don't know where the dy/dx comes from
7. (Original post by Alen.m)
this is the part i don't understand . here's how i do it which gives me the wrong answer : d/dx of y^2 is equal to 2y and 2y. x would give you 2xy . i don't know where the dy/dx comes from
Actually .
8. Use the chain rule. y is defined in terms of x - it isn't just a constant. Thus you have to multiply through by dy/dx.

(Original post by Alen.m)
this is the part i don't understand . here's how i do it which gives me the wrong answer : d/dx of y^2 is equal to 2y and 2y. x would give you 2xy . i don't know where the dy/dx comes from
9. (Original post by Alen.m)
this is the part i don't understand . here's how i do it which gives me the wrong answer : d/dx of y^2 is equal to 2y and 2y. x would give you 2xy . i don't know where the dy/dx comes from
Have you covered the chain rule yet?
10. (Original post by B_9710)
Actually .
The original question was x*d/dx(y^2). Multiplying by the x gives 2xy*dy/dx, as required.
11. (Original post by Alen.m)
this is the part i don't understand . here's how i do it which gives me the wrong answer : d/dx of y^2 is equal to 2y and 2y. x would give you 2xy . i don't know where the dy/dx comes from
Because if you are being asked to differnetiate y^2 with respect to x (which is what d/dx is asking) you simply cannot do this as you cannot differentiate a function in respect to another function like that. So you have to implicity differnetiate where you use the forumla stated above.

To give you y^2' *dy/dx *x=

2xy dy/dx

If it was asking to differentiate x^2 with respect to x you can do this and is a common result of 2x, hopefully that makes sense?
12. (Original post by constellarknight)
The original question was x*d/dx(y^2). Multiplying by the x gives 2xy*dy/dx, as required.
I know, I was replying to a question that the OP asked after the original post.
13. (Original post by Calzs34)
Because if you are being asked to differnetiate y^2 with respect to x (which is what d/dx is asking) you simply cannot do this as you cannot differntiate a function in respect to another function like that. So you have to implicity differntiate where you use the forumla stated above.

To give you y^2' *dy/dx *x

If it was asking to differntiate x^2 with respect to x you can do this and is a common result of 2x, hopefully that makes sense?
used the chain rule to solve it but still not getting it here's how i done it
Attached Images

14. (Original post by constellarknight)
Use the chain rule. y is defined in terms of x - it isn't just a constant. Thus you have to multiply through by dy/dx.
am i missing something here?
Attached Images

15. (Original post by lukejoshjames)
Have you covered the chain rule yet?
yes i did but i still get the answer as 2xy d/dx
Attached Images

16. (Original post by Alen.m)
used the chain rule to solve it but still not getting it here's how i done it
(Original post by Alen.m)
am i missing something here?
Try watching this video, you've made a mistake in the way you've differntiated, hopefully this clears it up:

If you're still confused reply back, but it's better to work it out yourself imo
17. (Original post by Alen.m)
yes i did but i still get the answer as 2xy d/dx
You do not actually cancel the dy's. The tells you to differentiate with respect to y and then you multiply through by dy/dx.
18. (Original post by B_9710)
You do not actually cancel the dy's. The tells you to differentiate with respect to y and then you multiply through by dy/dx.
thanks man i got it now
19. (Original post by Calzs34)
Try watching this video, you've made a mistake in the way you've differntiated, hopefully this clears it up:

If you're still confused reply back, but it's better to work it out yourself imo
the video was perfectly clear thanks

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