## anonymous 5 years ago Can anyone break down this into steps for me i need to find dy/dx by implicit differentiation

1. anonymous

$2\sqrt{x}+\sqrt{y}=5$

2. anonymous

ok So i am thinking

3. anonymous

$1/2x+1/y$

4. anonymous

Differentiate each term D/dx 2sqrt(x) = 1/sqrt(x) D/dx sqrt(y) = 1/2sqrt(y) * dy/dx D/dx 5 = 0 leaving $1/\sqrt{x} +1/2\sqrt{y}* dy/dx =0$ solve for dy/dx by subtracting 1/sqrt(x) and multiplying 2sqrt(y) $dy/dx =-2\sqrt{y}/\sqrt{x}$ in terms of x we have y = (5-2sqrt(x))^2 substitute this into above equation giving $dy/dx = 4-(10/\sqrt{x})$