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# CORE 4 differentiation watch

1. Find the value of dy/dx at the point (1,1) where 4xy^2 + 6x^2/y = 10

2. you've got differentiate implicitly
3. (Original post by Robofish)
you've got differentiate implicitly
Yeah i know you have to do that, but i dont really get it .
4. Use the product rule to differentiate (with respect to x) 4xy^2, then the quotient rule to differentiate(again wr.t. x) (6x^2)/y. The sum of these two derivatives will equal the derivative of 10 (ie 0).

Remember that
5. (Original post by namedeprived)
Use the product rule to differentiate (with respect to x) 4xy^2, then the quotient rule to differentiate(again wr.t. x) (6x^2)/y. The sum of these two derivatives will equal the derivative of 10 (ie 0).

Remember that
i dont know when you have to write dy/dx after you differentite it using the product and quotient rule
6. (Original post by klgyal)
i dont know when you have to write dy/dx after you differentite it using the product and quotient rule
4xy^2 is a product of 4x and y^2. The derivative of 4x (wrt x) is 4. Now let u=y^2

du/dy = 2y

Using the chain rule,

(du/dx)=(du/dy)(dy/dx) = (2y)(dy/dx)

So the derivative of y^2 (wrt x) is (2y)(dy/dx). So by the product rule, the derivative of 4xy^2 (wrt x) is 8xy(dy/dx) + 4y^2

Do you understand now?
7. thanks i get it now

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