Using implicit differentiation find dy/dx

[fringe lava]

what are you having an issue with

[unique badge]

finding dy/dx

[fringe lava]

thats fine, so you wanna start by differentiating with respect to x

do you know how to implicitly derive functions?

[unique badge]

yeah derivative of everything right

and everywhere there is a y you put a dy/dx because of the chain rule

[fringe lava]

yeah exactly

[unique badge]

would i just use algebra after that

to isolate dy/dx

[fringe lava]

yeah its pretty straight forward

tell me if you run into any issues

[unique badge]

ohhh ok

i see

if i was to set dy/dx equal to zero would that be where the original function has a horizontal slope

[fringe lava]

yes since the derivative basically gives you a rough estimation of the slope at each point

isolating the dy/dx term just makes everything easier to work with

[unique badge]

would dy/dx be equal to (-9x+18)/(4y+12)?

i think u could simplify it a little more

[fringe lava]

im pretty sure thats correct

[fringe lava]

not that i'm aware of, if you divide by 2 there'll be fractions

[unique badge]

factor out a 2 from the top and bottom then cancel it out?