Solve Implicit Functions: dy/dx of y^2+2y=x^3+3x-1

[madmike159]

Homework Statement

Find dy/dx of y^2+2y = x^3+3x-1

Homework Equations

The Attempt at a Solution

I devided both sides by y so i got y+2 = x^3+3x-1/y
then differentiating i got dy/dx = 3x^2 +3 / dy/dx

I don't think this is right
thanks for any help

 

[Office_Shredder]

What you should have gotten was

dy/dx = 3x² + 3 + 1/y²*dy/dx

As when you differentiate 1/y with respect to x, by the chain rule you get 1/y²*dy/dx To avoid y's in the denominator, it's probably better to start by differentiating rather than dividing both sides by y (you also put off corner cases where y=0 to be dealt with later... and procrastination is always good)

 

[madmike159]

ty