Question

Hello, any calculus one guru?

Answer 1

Hi @koome ,
\(\huge \color{red}{\text{Welcome to Open Study}}\ddot\smile\)

Can you post the problem you have difficulty with ?
i can try to help you :)

Answer 2

Aren't we all :D

Answer 3

ok, this x2+2xy-2y2 +2y2 + x=2 find the gradient of a curve at point ( -4 1)

Answer 4

Hatnn are u there?

Answer 5

yes, do you know how to find gradient ?

Answer 6

its same as slope,
so, first can you find dy/dx(or y') for x2+2xy-2y2 +2y2 + x=2 ?
using implicit differentiation ?

Answer 7

Not, what is confusing me is presence of y in the function..

Answer 8

don't worry about that, if you know chain rule,

d/dx (y^2) = 2y dy/dx

Answer 9

d/dx(y^2)=0

Answer 10

not actually

Answer 11

if y is the function of x, then
d/dx (y^2) = 2y dy/dx

Answer 12

Ok, let me revisit my notes. thanks

Answer 13

yes . if y is the function of x, then d/dx (y^2) = 2y dy/dx
but if y isn't function of x then d/dx (y^2)=0

Answer 14

if x2+2xy-2y2 +2y2 + x-2=f(x,y)=Z
x,y independent variable and Z dependent variable

Answer 15

here, y is indeed the function of x

Answer 16

aha OK

Answer 17

for 2xy, you'll need product and chain rule, both :)

Answer 18

lets take it term by term

x^2 ---->2x
2xy ----> try ??
-2y^2 -----> -4y dy/dx
+2y^2 ---->+4y dy/dx
x ----->1
2 ----->0

Answer 19

What about 2xy?

Answer 20

product rule,
\(\Large (xy)' = x'y + xy'\)

Answer 21

and x' = 1 since we are differentiating with respect to x

Answer 22

is your question really \(x^2+2xy-2y^2 +2y^2 + x=2\)
or something else ?

Answer 23

we have only -2y^2+x, no +2y^2

Answer 24

okk,
so,
\( \Large 2x +2 (y +x \dfrac{dy}{dx}) - 4y\dfrac{dy}{dx}+1=0 \)


did you get till here ? anydoubts anywhere ?

Answer 25

No doubts.. Great

Answer 26

now you can just put ( x= -4, y= 1) in that and find dy/dx
that will be your gradient :)

Answer 27

Just a quiz 2(Y+X dy/dx) ( 2+2) whats hapens to these values?

Answer 28

Hello... are u there?

Answer 29

yes,
and how did you get that ?
there's also =0 , the right side

Answer 30

\(\Large 2(-4) +2 (1 +(-4) \dfrac{dy}{dx}) - 4(1)\dfrac{dy}{dx}+1=0\)

Answer 31

only dy/dx is unknown :)

Answer 32

Ok, Thanks alot

Answer 33

you're welcome ^_^
if you want me to verify the final answer, tell me what you got.

Answer 34

Hello, is it -17

Answer 35

no

Answer 36

Whay please?

Answer 37

\(\Large 2(-4) +2 (1 +(-4) \dfrac{dy}{dx}) - 4(1)\dfrac{dy}{dx}+1=0 \\ \large -8+ 2(1-4y')-4y'+1 = 0 \\ \large -7 +2 -12y' =0 \\ \large -5-12y'=0

\\ \large y' = \dfrac{-5}{12} \)

Answer 38

ask if anymor doubts.

Answer 39

You replace x value -4 to y value ie ( 1-4y'?

Answer 40

since we need gradient at point (-4,1)

i replaced x by -4
and y by 1

Answer 41

Then y do we have 2( 1+ -4 dy/dx)

Answer 42

oh, i thought you got this

\(\Large 2x +2 (y +x \dfrac{dy}{dx}) - 4y\dfrac{dy}{dx}+1=0\)

then
putting x =-4, y=1, we get
\(\Large 2(-4) +2 (1 +(-4) \dfrac{dy}{dx}) - 4(1)\dfrac{dy}{dx}+1=0\)

isn't it ?

Answer 43

I have a problem only with the this part 2( x+y) where do we get y value as negative-4 ?
I think when we replace x= -4 and y 1?

Answer 44

yes, we did, we never replaced y by -4

Answer 45

Please make me understand ...

Answer 46

Then y do we have y as -4

Answer 47

\(y+x (dy/dx) \implies 1+(-4)(dy/dx)\)

we never have y as -4

Answer 48

why do u think we have y as -4 ?

Answer 49

so we differentiate the x y, = 1+1 then we replace the values( 1+-4) what we get is the

Answer 50

Still i cant understand ? y-4 for the second term yes coz -2y^2 = -4y

Answer 51

x^2 ---->2x
2xy ----> 2(y + x dy/dx)
-2y^2 -----> -4y dy/dx
x ----->1
2 ----->0

which one did u not understand ?

Answer 52

2xy why do we get y as -4

Answer 53

product rule

Answer 54

-2*2

Answer 55

2xy ----> 2(y + x dy/dx)

put x = -4 , y= 1

2(1- 4(dy/dx))

Answer 56

err power rule

Answer 57

I think y' would be an easier notation for koome to understand, hartnn,

Answer 58

2xy ----> 2(y + x y')

put x = -4 , y= 1

2(1- 4 y')

Answer 59

if you're still confused, try it by yourself and give us the steps, we will spot the error in your working, if any.

Answer 60

^ Just as Hartnn mentioned, let us know if you're still having trouble understanding this. The implicit differentiation can get tricky, but when you get the hang of it, you'll be zooming :P.

Answer 61

Thanks 4 this help an trying to figure out i will get back to u.. revisiting notes

Answer 62

good luck! :)

Answer 63

Thanks alot. hope am allowed to come back any time.. You are awesome ....

Answer 64

You are always welcome!

Answer 65

will be glad if you come back :)

Answer 66

Hello, got it thanks... y though do we have -12y instead of -8 y?
because -4

Answer 67

-4 is 8

Answer 68

Sorry which part is this?

Answer 69

sory -8

Answer 70

2*(-4)?

Answer 71

Look at what Hartnn did, that should help ya :P

Answer 72

Or tell me what part you lost him?

Answer 73

This part -8+2(1-4y')-4+1
y do we have 12y?

Answer 74

instaed of -
8Y