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Help: Find the slope of the tangent line to the curve (attached below)

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I'm a little confused, where do i know to put d/dx and when to directly do the derivative..
use implicit differentiation to find dy/dx and exaluate at the given point.

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Other answers:

i did, but thats where im confused... it's like i can take the derivative of -3x^2 but then should i put d/dx next to it... or just simply leave it -6x
im getting mixed up.
then also 3xy... derivative or not... i know i have to put d/dx
if it's a function of x then take the derivative of the function and multiply by its differential, dx. Same with y. example. for x^2 you'd get 2x*dx, for y^2 you'd get 2y*dy
for xy, use the product rule. y*dx + x*dy
right, okay. let me try again
so first it would be -6x*d/dx right?
no... just -6x*dx
and what about the 3 do i leave it out? and use product rule with xy?
3 is a constant so it oges along for the ride. also, d/dx is an operator. it says to take the derivative of whatever follows wrt x.
with respect to x..
i dont know ive been using d/dx whenever i see an x and dy/dx for a y
dx is the differential of x... the change in x, if you will
you could do dx/dx everytime you take a derivative of a function of x and dy/dx for a function of y... that's okay. but dx/dx is just 1.
ok yes:) now we're on the same pg
for the middle part, is it, 3x*dx/dx+y*dy/dy?
= 3y + 3x*dy/dx
i 've got to go... so you can at least check... you should get 3 as the final answer. Good luck!
thank you, i appreciate it.

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