Question

Find d2y/dx2 in terms of x and y.
y^4 = x^5
d2y/dx2 =

Answer 1

Find dy/dx
first.
Then differentiate it again to get d2y/dx2

Answer 2

4y^3y'=5x^4
y'=5x^4/4y^3=5x/4y*xy/xy

Answer 3

5y/4x*x^5/y^4= 5y/4x

Answer 4

y"= 4x(5y')-5x(4)/16x^2

Answer 5

i dont know how can i finish it :/

Answer 6

y^4 = x^4
dy/dx
4y^3y' = 5x^4
y' = (5x^4)/(4y^3)
\[y'' = \frac{ 20x^34y^3 - 5x^412y^2y' }{ (4y^3)^2 }\]
Plug in y' into this and simplify it to get y'' :)
Simplify if needed.

Answer 7

\[\large y'' = \frac{ 20x^34y^3 - (5x^412y^2*\frac{ 5x^4 }{ 4y^3 }) }{ 16y^6 }\]
Just simplify it out now.

Answer 8

40y/16x^2

Answer 9

@shamil98 right

Answer 10

i dont know how can i do the top @shamil98