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

if we implicitly differentiate $\displaystyle y^3-xt^2=2$

is this the right approach?

$\displaystyle d/dy*dy/dx-[d/dx(x)*y^2+d/dy*x]$

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