Question

find second derivative if (x-5)^5+(y-2)^5=64

Answer 1

f1{x,y} = 5(x-5)^4

f11{x,y} = 20(x-5)^3

Answer 2

f2{x,y} = 5(y-2)^4

f22{x,y} = 20(y-2)^3

Answer 3

5(x-5)^4 + 5(y-2)^4 dy/dx =0 ist derivative

Answer 4

right, so long as we imply that y is a function of x

Answer 5

yes,, maybe we can let snenlaha do the 2nd derivative hehehehe

Answer 6

maybe :)

Answer 7

i couldn't continue from the first to the 2nd derivative

Answer 8

but do you know the process of the ist that i did?

Answer 9

yes i do and i got it the same as yours

Answer 10

ok try the second so that you cn have confidence in yourself

Answer 11

do i need to make dy/dx a subject of the formula

Answer 12

try to arrange them first, start with dy/dx =

Answer 13

you can; y' just derives to y''; just be sure to use it as such in its product rule

Answer 14

yes thats the other way doing it,, either one will arrive at the right solution

Answer 15

to implicit it again would be easier; no quotient ruls to fight with i believe

Answer 16

ok thats rigth....try implicitly ..

Answer 17

5(x-5)^4 + 5(y-2)^4 y' =0

20(x-5)^3 + 5(y-2)^4 y'' + 20(y-2)^3 y' y' = 0 then if it works out that way :)

Answer 18

Dx(5(x-5)^4) + Dx(5(y-2)^4 dy/dx) =Dx(0).......ok amistre did it now hehehehe

Answer 19

i got no idea if its right :)... other than the obvious typos that is

-20[(x-4)^3 + (y-2)^3 y'^2]
y'' = ------------------------- right?
5(y-2)^3

Answer 20

-20/5 reduces..... and y' = whatever it equals lol

Answer 21

the answer is suppose to be: y''=(-256(X-5)^3)/(y-2)^9

Answer 22

dy/dx=-(x-5)^{4}/(y-2)^{4}\[d ^{2}y/dx ^{2}=-256(x-5)^{3}/(y-2)^{5}\]

Answer 23

it prolly simplifies to that then lol...

Answer 24

yeah ,... thats the answer to it Snenhlala....try to practice till you arrive to that answer

Answer 25

sorry the denominator for the second derivative should read (y-2)^9

Answer 26

did you used product rule or quotient rule to find 2nd derivative

Answer 27

i did mine in quotient rule

Answer 28

use the quotient rule and sub for dy/dx

Answer 29

mulitply each term by (y-2)^4
then factor -4(x-5)^3(y-2)^3
this will leave (x-5)^5+(y-2)^4 which equals 64 (from the original equation)

Answer 30

should read (x-5)^5+ (y-2)^5 which equals 64

Answer 31

should i start to multiply from the 1st derivative or from the origin equation?

Answer 32

multiply the second derivative

Answer 33

by (y-2)^4

Answer 34

y'= -(x-5)^4 / (y-2)^4
-4(y-2)^4 (x-5)^3 - 4(x-5)^4 (y-2)^3 y'
y"= ----------------------------------- now subst. y ' in this equqtion
((y-2)^4)^2

-4(y-2)^4 (x-5)^3 - 4(x-5)^4 (y-2)^3 [-(x5^4)/(y-2)^4]
y"= -------------------------------------------------------------
((y-2)^4)^2


-4(y-2)^4 (x-5)^3 + 4(x-5)^8 (y-2)
y"= -----------------------------------
(y-2)^8

Answer 35

-4(y-2)^4 (x-5)^3 + 4(x-5)^8/(y-2)
y"= ----------------------------------- ... sorry its divided by y-2
(y-2)^8

Answer 36

-4(y-2)^5 (x-5)^3 + 4(x-5)^8
y"= -----------------------------------
(y-2)^9

Answer 37

-4 (x-5)^3 [(y-2)^5 + (x-5)^5]
y"= -----------------------------------
(y-2)^9

Answer 38

-4 (x-5)^3 [64]
y"= --------------
(y-2)^9
57 seconds ago

Answer 39

-256 (x-5)^3
y"= --------------
(y-2)^9

Answer 40

well i think thats it hehehe

Answer 41

thank you

Answer 42

w.c.

Answer 43

did you arrived in the same procedure?

Answer 44

and of course the same answer? lol

Answer 45

yes i did arrive but it too tricky

Answer 46

yeah kind of hehehe,,