Urgent Differentiation Question

[kpax]

how do you differentiate

2x^2 - 4xy + 3y^2 = 3 ?


cheers this is really urgent and id really appreciate a quick reply

[shukla]

exactly what do you want to do ?

[kpax]

its a question and you are suppose to differentiate it and find its gradient at (2,1)

cheers

[shukla]

place x = 2 and y=1 and then you will get solution.

[kpax]

how does that help? i need to differentiate it

[shukla]

i think you will get it at

http://www.bbc.co.uk/education/asgur...in/index.shtml

[Mattywoo2]

If we can assume y is a function of x, and we are differentiating wrt x, then we make use of implicit differentiation and the product rule.

2x² - 4xy + 3y² = 3

Differentiate both sides wrt x.

4x - {4x(dy/dx) + 4y} + 6y(dy/dx) = 0

4x - 4x(dy/dx) - 4y + 6y(dy/dx) = 0

Factor out the dy/dx

(dy/dx)(6y-4x) + 4x - 4y = 0

Simplify

dy/dx = (4y-4x)/(6y-4x)

Now plug in x=2 and y=1

dy/dx|(2,1) = gradient at (2,1) = 2

If you need any concepts explained please give me a shout. AND RATE ME!!

All the best, Matt