implicit differentiation problem step by step (tell me if my concepts are wrong plz)

if we implicitly differentiate

is this the right approach?

which means (I intend it to mean)

the derivative of y with respect to itself TIMES the derivative of y with respect to x MINUS [the derivative of x with respect to itself times y^2 PLUS the derivative of y with respect to itself TIMES x]

firstly did I write in math what I wrote in english? and secondly is it correct?

thanks!

Re: implicit differentiation problem step by step (tell me if my concepts are wrong p