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anonymous
 4 years ago
Implicit differentiation:
y + 3xy 4 = 0
anonymous
 4 years ago
Implicit differentiation: y + 3xy 4 = 0

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dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.3take derivative of each term as you would normally, except whenever you differentiate y multiply by y'

lalaly
 4 years ago
Best ResponseYou've already chosen the best response.0y'+3y+3xy'=0 y'+3xy'=4 y'(1+3x)=4 y'=4/(1+3x)

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.3y'+3y+3xy'=0 y'+3xy'=4 < **4 should be 3y ** y'(1+3x)=4 < y'=4/(1+3x) <

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Thank you, that is what my book says as well. I'm a little bit lost though. I get that the derivative of the y = 1, multiply that by y\[\prime\], but then 3xy, why does that become 3xy[\prime\]? And the 4, how does that become 3y[\prime\]?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Oh, am I to treat it as (3xy)\[^{1}\]?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ah sorry, my equation formatting is a mess :\

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.3its the product rule (fg)' = fg' +f'g

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.3(3xy)' = (3x)*y' + (3x)'*y = 3xy' + 3y

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I see. So then the 4 still becomes zero, as in other cases?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Okay, thank you very much :D That will be very helpful for the next problems, hopefully I can manage them on my own.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Just double checking before I continue, for example: 3*x^3*y^2 would become 3x^3(2y) + 3(3x^2)(y^2), correct?

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.3yes but don;t forget about the y'

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0So, each of those two terms is also multiplied by y prime? I'm not to clear on what you mean.

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.3no only the term where you differentiated y (1st term) 3x^3(2y)y' because 2y came from differentiating y^2

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ah okay. So, I multiply by y(prime) whenever I differentiate y.
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