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**Question:**

Find dy/dx by implicit differentiation

4x^2 + 3xy - y^2 = 6

**Attempt:**

Ok, just a forewarning that I suck at differentiations, limits, what-not, so..

Following my textbook, it says I should Differentiate both sides of the equation

So...

(d/dx)(4x^2 + 3xy - y^2) = (d/dx)(6)

(d/dx)(6) = 0, so I have to solve the derivatives of the other side..

Now, this is the part that I'm unsure about, so please guide me here:

(d/dx)(4x^2) = 8x right? Since I bring down the two and subtract 1

Ok, so.. (d/dx)(3xy), using the chain rule which is f(g(x)) = f'(g(x))*g'(x), I figured:

y(...) is the outer function and 3x is the inner funtion

thus, making it (y(3x))' * (3x)' = (dy/dx)(3x) * 1???

Can someone please clarify that last part I wrote for me? Also, it'd be great if someone can clarify the difference and meaning between dy/dx, d/dx, and d/dy..

Then I'll try and move on XD

Please and thank you for your time XD

PS: I do realise I haven't got through the whole question, but I will, once the above is clarified as correct, etc. :D