Sense I had nothing to do I thougt I do some math but I seem to have forgot derivative...
"Determen dy/dx in (1,2) for 4xy^2 - 12xy + 13 = 5x"

4 d/dx (xy^2) - 12 d/dx(xy) + d/dx(13) = d/dx(5x)

4(d/dx(x) + x d/dx(y^2)) - 12(d/dx(x) + x (d/dx(y)) + d/dx(13) = d/dx(5x)

4(d/dx(x) + x d/dy(y^2) dy/dx) - 12(d/dx(x) + x (d/dy(y) dy/dx) + d/dx(13) = d/dx(5x)

4(1 + x*2y^(2-1) dy/dx) - 12(1 + x*1 dy/dx) + 0 = 5

4+4x2y dy/dx - 12-12x dy/dx = 5

dy/dx + dy/dx = (5-4+12)/(4x2y-12x)

2 dy/dx = 13/4 <- This is the right awnser

dy/dx = 13/8 <- This is wrong

Anyone that can explain for a dumb kid what he is doing wrong?
Sure, I'll give it my best shot. And anyone that shows how they work through it before asking is certainly good in my books. Also, implicit differentiation can really stink.

Note: For clarification, I write dy/dx as y'

Here are my steps and interpretation:

Original:
4xy^2-12xy+13=5x

Derive both sides implicitly:
d/dx(13)-d/dx(12xy)+d/dx(4xy^2) = d/dx(5x)
0-d/dx(12xy)+d/dx(4xy^2) = d/dx(5x)

Pull out constants:
-12(d/dx(xy))+4(d/dx(xy^2)) = d/dx(5x)

u*v = vu'+uv'
4(x(d/dx(y^2))+d/dx(x)y^2)-12(x(d/dx(y))+d/dx(x)y) = d/dx(5x)

d/dx(x) is 1
4(x(d/dx(y^2))+y^2)-12(x(d/dx(y))+y) = d/dx(5x)

d/dx(y) is y'
4(x(d/dx(y^2))+y^2)-12(xy'+y) = d/dx(5x)

d/dx(y^2) is 2(d/dx(y)y)
4(x(2(d/dx(y)y))+y^2)-12(xy'+y) = d/dx(5x)

d/dx(5x) = 5
4(2xyy'+y^2)-12(xy'+y) = 5

Expand left hand side of equation:
8xyy'+4y^2-12xy'-12y = 5

Get y' on left side of equation:
8xyy'-12xy' = 5-4y^2+12y

Factor out y' on left side of equation:
y'(8xy-12x) = 5-4y^2+12y

Divide by 8xy-12x:
y' = (5-4y^2+12y)/(8xy-12x)

Therefore, if y is 2 and x is 1, y' = 13/4

Hopefully this helps! Feel free to ask any follow-up questions.

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