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# C4 differentiating question.... watch

1. Can someone help me out with this? (explaining it in as much detail as possible please).

The curve C has equation
13x^2 + 13y^2 - 10xy = 52

Find an expression for dy/dx as a function of x and y, simplifying your answer.

Thanks.
2. just differentiate each part so you get 16x + 26y(dy/dx) - 10y -10x(dy/dx)= 0
everytime you differntiate a y put in dy/dx after it, when differntiating the -10xy just use the product rule to get -10x(dy/dx)-10y.

to simplify take everything that isnt with dy/dx to get:-
26y(dy/x)-10x(dy/dx)=10y-16x,
take out a factor of dy/dx ont he lhs
dy/dx(26y-10x)=10y-26x
just bring it over to ther otehr side
dy/dx=(10y-26x)/(26y-10x)

Thats it i think although id get someone to check, im prone to making stupid mistakes.
3. (Original post by Goody1)
just differentiate each part so you get 16x + 26y(dy/dx) - 10y -10x(dy/dx)= 0
I think thats meant to be:

26x + 26y(dy/dx) - 10y -10x(dy/dx)= 0
4. I think I've done it right ...

Attached scan of it.
Attached Images

5. Thanks for that - where did the 16 come from though? Should it be 26?
6. (Original post by Goody1)
dy/dx=(10y-16x)/(26y-10x)
Then just simplify to dy/dx = (5y-13x)/(13y-5x)
7. (Original post by Laura_M)
Thanks for that - where did the 16 come from though? Should it be 26?
yes
8. As a check:

13x2 + 13y2 - 10xy = 52

=> 26x + 26y(dy/dx) - [ 10x(dy/dx) + 10y ] = 0

=> 26x + 26y(dy/dx) - 10x(dy/dx) - 10y = 0

=> dy/dx(26y - 10x) + 26x - 10y = 0

=> dy/dx(26y - 10x) = 10y - 26x

=> dy/dx = (10y - 26x)/( 26y - 10x)

Which means I have the same as you bar you have a -16x not a -26x.

You differentiated 13x2 to 16x. It is 26x.
9. Thank you - you're all amazing!!
10. Woah! Five posts all at once.
11. lol indeed and about the 16x and 26x told you i made stupid mistakes lol my one big downfall in this subject is stupid errors that i do by moving onto the next stage of the question while ims till writing out the part before.

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