Question

5y3 – 4x3y2 = 6 implicitly derive

Answer 1

derive means like to find
so what do you want to find?

Answer 2

i think you mean implicitly differentiate

Answer 3

yes lol

Answer 4

lol

Answer 5

so what is (5y^3)'=?

Answer 6

alright how to figure this out

Answer 7

15y^2

Answer 8

15y^2*y'

Answer 9

remember to keep your derived bit around, they are needed later :)

Answer 10

\[(4x^3y^2)'=4(x^3y^2)'=4(3x^2y^2+x^3(y^2)')\]

Answer 11

they really should teach you to keep them at the start, and let you do the mental math in eliminating them if need be...

Answer 12

what rule did i use there?

Answer 13

chain rule

Answer 14

...id say it begins with a pro, and ends with a duck, rule

Answer 15

no i havent used the chain rule yet (but for (5y^3)' we did)
we are looking at (4x^3y^2)' now

Answer 16

doing online school for undergrad amistre dont trying to understand how to learn through these study groups before i head out again

Answer 17

trying*

Answer 18

right amistre product rule!

Answer 19

but what is
\[(y^2)'=?\]

Answer 20

what rule do we need to apply here?

Answer 21

haha guys are quick

Answer 22

we need to apply chain rule

Answer 23

yes so
we do derivative of inside * derivative of outside
y' * 2y^1
=y'2y

Answer 24

5y3 – 4x3y2 = 6

Answer 25

so derivative of 4x^2

Answer 26

so anyways when we put it altogether we have
\[15y^2y'-4(3x^2y^2+x^3y'2y)=0\]

Answer 27

wolfram simplified it to 15y^2-8x^3y=0

Answer 28

\[15y^2y'-12x^2y^2-8x^3yy'=0\]
\[y'(15y^2-8x^3y)=12x^2y^2\]
\[y'=\frac{12x^2y^2}{15y^2-8x^3y}\]