Check request: Implicit Differentiation

[DollarBill]

Homework Statement

Find the value of dy/dx at x=2 when

x²+xy=5

The Attempt at a Solution

To find y:
2²+2y=5
y=1/2

To find dy/dx:
2x(dx/dx)+x(dy/dx)+y(dx/dx)=0

2x+x(dy/dx)+y=0

(dy/dx)=(-2x-y) / x

Plug in y and x:
dy/dx=-2(2)-(1/2) / 2

dy/dx=-9/4 when x=2

 

[D H]

Correct.