Question

Find dy/dx by implicit differentiation.
sqrt(x+y)=4 +x^2y^2
please show all steps

Answer 1

differentiate the left side then differentiate the right side...where are you having trouble?

Answer 2

I'm not sure where i'm going wrong. But I cant isolate y, so i think that maybe i'm going wrong from the start with differentiating each part?

Answer 3

this is what i got when I differentiated it:
1/(2sqrt(x+y))=2xy^2+(x^2)2y * (x^2)(y')

Answer 4

Left side: y'/ 2√( x + y)
Right side: 2x²y *y' + 2xy²

Answer 5

@darkmare Questions?

Answer 6

can you possibly show how you got that? Mine differentiated from that a fair bit

Answer 7

Left side: you missed y' ( take dy/dx )
Right side: (x²y² )'
Let u = x² --> u' = 2x
v = y² --> v' = 2y y'
Now just plug into u'v + uv' = 2x²y *y' + 2xy²

Answer 8

do i then isolate for y' to find dy/dx?

Answer 9

Now switch 2x²y *y' to the left side, then factorize y'

Answer 10

can you write out what the equation would be? i'm not following very well.
would you have 2xy^2+x^2(2yy')=2x^2y(y') + 2xy^2?
or 2x^2y(y') +2xy^2=0?