How to Correctly Apply Implicit Differentiation?

[5ymmetrica1]

Homework Statement

For the curve x²+3xy+y² = 5

show that $\frac{dy}{dx} =- \frac{2x+3y}{3x+2y}$

Homework Equations

N.A.

The Attempt at a Solution

2x + 3xy + 2y$\frac{dy}{dx}$ = 0

3x + 2y $\frac{dy}{dx}$ = -2x+ 3y

∴ $\frac{dy}{dx} =- \frac{2x+3y}{3x+2y}$

have I done this correctly?

 

[ehild]

Homework Statement

For the curve x²+3xy+y² = 5

show that $\frac{dy}{dx} =- \frac{2x+3y}{3x+2y}$

Homework Equations

N.A.

The Attempt at a Solution

2x + 3xy + 2y$\frac{dy}{dx}$ = 0

3x + 2y $\frac{dy}{dx}$ = -2x+ 3y

∴ $\frac{dy}{dx} =- \frac{2x+3y}{3x+2y}$

have I done this correctly?

No. You forgot to differentiate 3xy, or you forgot to write it out, and there are other problems with parentheses.

ehild