Question

Help ~ Find the gradient of the curve at (2,1) .
2x^2 - 4xy +3y^2 = 3

Answer 1

\[2x ^{2} - 4xy + 3y ^{2} = 3\]

Answer 2

the gradient defines equations for the vector components of a normal to a surface

Answer 3

but it has a different meaning in R^2

Answer 4

ok i catch no ball .

Answer 5

what is a gradient? since it has different definitions

Answer 6

lols the question just wrote that. its a 4marks question of Alvl pure maths P3 !!

Answer 7

calculus 1 by chance?

Answer 8

answer was 2 and i dunno how the flutter it came

Answer 9

please dont use that kind of language in here, its inappropriate and we have filters to catch it.

Answer 10

most likely this is by implicit differentation

Answer 11

ok , i apologise mate . ;D

Answer 12

do you know how to take a derivative of a function?

Answer 13

yes

Answer 14

u meant differentiation right ? of which ones ?

Answer 15

2x^2 - 4xy +3y^2 = 3 take derivatives term by term

whats the derivative of 2x^2 with respect to x?

Answer 16

dude please kindly take your time and write me the working very nicely.
4x

Answer 17

4x is good

what is the derivative of -4xy with respect to x? use the product rule

Answer 18

-4y

Answer 19

recall the product rule:

[fg]' = f'g + fg'

[-4xy]' = -4x'y -4xy' ; but x' = 1

-4y -4xy'

Answer 20

ohh

Answer 21

omg its getting confusing

Answer 22

please just write me the working and how u got the answer please.
kamsamhamnida !

Answer 23

2x^2 - 4xy +3y^2 = 3; so far we got: 4x 4y -4x y' + [3y^2]' = [3]'

what the derivative of 3y^2 with respect to x?

Answer 24

피이팅 !

Answer 25

we are alomst done, just hang in there

Answer 26

hmmmm...........

Answer 27

take a guess, what would this derive to if the y was an x?

Answer 28

i still don't get it . =[

Answer 29

what is the derivative of : 3x^2 ??

Answer 30

6x

Answer 31

good, but but when we dont have the x, we pop out a y'

3y^2 derives to 6y y'

Answer 32

uh huh

Answer 33

and the derivative of that constant is 0 as usual

2x^2 - 4xy +3y^2 = 3 derives to; 4x -4y -4x y' + 6y y' = 0

plug in your point values for x and y, and solve for y'

Answer 34

oh after u get that u only sub in for x values ??

Answer 35

(x=2,y=1)

4x -4y -4x y' + 6y y' = 0

4(2) -4(1) -4(2) y' + 6(1) y' = 0

8 -4 - 8y' + 6y' = 0

8 -4 + y'(-8+6) = 0

4 + y'(-2) = 0

y'(-2) = -4

y' = -4/-2 = 2

Answer 36

since we have xs and ys, and the point defines our x and y; plug in and solve

Answer 37

ohhh~

Answer 38

so the y=2 is the final answer which is the gradient right ?

Answer 39

y' = 2 is the slope of the tangent line at the given point, the gradient, yes

Answer 40

ohh

Answer 41

hahahs i do kind of get it , i'll try more of this questions !!
THANK YOU for the HELP !! ;DD sarang hamnida.~
사랑합니다 !

Answer 42

youre welcome, and good luck ;)

Answer 43

muacks!!