differentiation parametric

[regal robin]

Show the full question

wait

use product rule

[vagrant bloom]

i don't need product rule

[vagrant bloom]

that is the full question

[regal robin]

?

Use the product rule on tcost

[humble kernel]

There’s two constants multiplying by each other
t x cost

[vagrant bloom]

ngl u lost me here already

[humble kernel]

which part

i can explain it

[vagrant bloom]

i'm sorry but i can't read that

[regal robin]

just use the product rule lmao

And do it normally

[humble kernel]

😭

[vagrant bloom]

sorry but which one is u and which one is v?

[humble kernel]

I tried making it neater

[regal robin]

How can u not read their writing

[humble kernel]

cos

[humble kernel]

oops it was y - (-pi)

[vagrant bloom]

i'm sorry but i cannot follow any of that

like i don't get what stage ur moving into and why

[humble kernel]

do you know the formula to differentiate parametric

[vagrant bloom]

like how is dv/dt = 1 AND -sint?

yes

[humble kernel]

product rule

its t multiplied by cos

[humble kernel]

du/dt is 1
dv/dt is -sin

[vagrant bloom]

how are they both the same?

[humble kernel]

it was meant to be du for the one on the left

[vagrant bloom]

can u just walk me through it instead bc i'm not gonna be able to understand whatever u wrote on here

[humble kernel]

okay

x = 3 - 2sint

can you differentiate that

[vagrant bloom]

yeah

-2cost

[humble kernel]

okay nice

thats dx/dt

[vagrant bloom]

dx/dt is that

[humble kernel]

now y = t x cost

[vagrant bloom]

yeah so dt/dx is -1/2cost

let u = t and v = cos t

du/dt is 1

[humble kernel]

i dont think you need to flip it over, its meant to be dx/dt

[vagrant bloom]

for v:

v= cos u bc u = t
--> dv/dt = -sint

[vagrant bloom]

yes u do

dy/dx = dy/dt * dt/dx

so u'v + uv'

[humble kernel]

oh yeah mb

[humble kernel]

okay nice

[vagrant bloom]

--> cost -tsint

that's for the differential of parametric y

[humble kernel]

yes

[vagrant bloom]

so then it's just -(cost - tsint)/2cost

[humble kernel]

-2

[vagrant bloom]

yeah that's what i said

[humble kernel]

its (cost-tsint)/-2cost

[vagrant bloom]

yeah but that's just the same as that

[humble kernel]

oh alr

[vagrant bloom]

still gonna get a negative anyways

[humble kernel]

okay now you can sub pi in

as t = pi

[vagrant bloom]

yeah great so that's the gradient

[humble kernel]

yeah

then you do y-1=m(x-x1)

[vagrant bloom]

yeah thanks got it from here