Question

Can anyone break down this into steps for me i need to find dy/dx by implicit differentiation

Answer 1

\[2\sqrt{x}+\sqrt{y}=5\]

Answer 2

ok So i am thinking

Answer 3

\[1/2x+1/y\]

Answer 4

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
\[dy/dx = 4-(10/\sqrt{x})\]