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

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

Mathematics
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f1{x,y} = 5(x-5)^4 f11{x,y} = 20(x-5)^3
f2{x,y} = 5(y-2)^4 f22{x,y} = 20(y-2)^3
5(x-5)^4 + 5(y-2)^4 dy/dx =0 ist derivative

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Other answers:

right, so long as we imply that y is a function of x
yes,, maybe we can let snenlaha do the 2nd derivative hehehehe
maybe :)
i couldn't continue from the first to the 2nd derivative
but do you know the process of the ist that i did?
yes i do and i got it the same as yours
ok try the second so that you cn have confidence in yourself
do i need to make dy/dx a subject of the formula
try to arrange them first, start with dy/dx =
you can; y' just derives to y''; just be sure to use it as such in its product rule
yes thats the other way doing it,, either one will arrive at the right solution
to implicit it again would be easier; no quotient ruls to fight with i believe
ok thats rigth....try implicitly ..
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 :)
Dx(5(x-5)^4) + Dx(5(y-2)^4 dy/dx) =Dx(0).......ok amistre did it now hehehehe
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
-20/5 reduces..... and y' = whatever it equals lol
the answer is suppose to be: y''=(-256(X-5)^3)/(y-2)^9
dy/dx=-(x-5)^{4}/(y-2)^{4}\[d ^{2}y/dx ^{2}=-256(x-5)^{3}/(y-2)^{5}\]
it prolly simplifies to that then lol...
yeah ,... thats the answer to it Snenhlala....try to practice till you arrive to that answer
sorry the denominator for the second derivative should read (y-2)^9
did you used product rule or quotient rule to find 2nd derivative
i did mine in quotient rule
use the quotient rule and sub for dy/dx
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)
should read (x-5)^5+ (y-2)^5 which equals 64
should i start to multiply from the 1st derivative or from the origin equation?
multiply the second derivative
by (y-2)^4
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
-4(y-2)^4 (x-5)^3 + 4(x-5)^8/(y-2) y"= ----------------------------------- ... sorry its divided by y-2 (y-2)^8
-4(y-2)^5 (x-5)^3 + 4(x-5)^8 y"= ----------------------------------- (y-2)^9
-4 (x-5)^3 [(y-2)^5 + (x-5)^5] y"= ----------------------------------- (y-2)^9
-4 (x-5)^3 [64] y"= -------------- (y-2)^9 57 seconds ago
-256 (x-5)^3 y"= -------------- (y-2)^9
well i think thats it hehehe
thank you
w.c.
did you arrived in the same procedure?
and of course the same answer? lol
yes i did arrive but it too tricky
yeah kind of hehehe,,

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