implicit differentiation

[indigo crown]

help w q1c pls.. 😭

[indigo crown]

<@&791435371564892232>

[hardy hearth]

if uno how to differentiate then I assume helping w just the first question could give u an idea on how to do the rest

I believe this is correct. lmk if it is wrong and if u need help on the rest!

[hazy nexus]

ye this is right

[indigo crown]

yes that’s correct for just normal differentiation but the topic i’m doing is implicit differentiation where y differentiates into dy/dx 😭 sorry if i didn’t make it clear enough

[hardy hearth]

ohh hmm I don't understand aha

maybe I havent learnt it. im sorry aha

[indigo crown]

OHHH it’s okay dw abt ☺️

[maiden fjord]

so if we take d/dx on both sides

$\frac{d}{dx}(5x^{2}y^{4} + 8x) = \frac{d}{dx}(2y^2)$

[fringe ridge]

David

[maiden fjord]

now if we use product rule for 5x^2y^4

so u = 5x^2, v = y^4
u' = 10x, v' = 4y^3 dy/dx

then it differentiates to
(20x^2)(y^3)(dy/dx) + (10x)(y^4)

so we have
(20x^2)(y^3)(dy/dx) + (10x)(y^4) + 8 = 4y dy/dx

get all the dy/dx's to one side

factor out and divide

[indigo crown]

NICE ONE - if u don’t mind can u just like help me start off this other q and i’ll try nd do the rest if ur not busy ofc 😭

[maiden fjord]

Ye sure

[indigo crown]

just q 3a and 8b - thanks again fr

[maiden fjord]

For 3a) just sub in x=1 and y = a

8b) find dy/dx first

[indigo crown]

ya, i got: dy/dx = 54 - 18xy/48y^2 + 9x^2

then replaced dy/dx with 0 to get: 0 = 54 - 18xy/48y^2 + 9x^2

[hazy nexus]

ik this wasn’t aimed at me but I learnt some new from this thank you 💀🙏🏿