Question

Find dy/dx by implicit differentiation

xy+4x+5x^2=3

Answer 1

Use product rule for first term
1*y+x y'

Answer 2

x*dy/dx + y + 4 +10x = 0
y + 4 +10x = -x * dy/dx
dy/dx = -(y + 4 +10x) / x

Answer 3

\[xy'+y+4+10x=3\] solve for y'

Answer 4

oops that is wrong

Answer 5

\[xy'+y+4+10x=0\] is more like it

Answer 6

mancub0 has it

Answer 7

one can also do it the quick way.
If we define \[F(x,y)=x\cdot y+4x+5x^2-3\]

then \[\frac{dy}{dx}=-\frac{\frac{\partial F}{\partial x}}{\frac{\partial F}{\partial y}}\]

\[=-\frac{y+4+10x}{x}\]