I so thankful for your help. Please help me expressing this expression compactly is there any pattern here?

sorry for posting the same question again. reason: the equation no. (2)

Thank you so very much for your help.

I was to solve, means find y as a function of x, equations like the following

y(x) = 7/8 * x + 1/2 * int (x*t*y(t)^2,t=0..1)

or

please help me here

we want a "remember table assignment for the first derivative evaluated at a point a1" for example

D(f)(a1):=0

but using this command maple creates a proc

for example using the command

f(a1):=0:

maple asks : 1. function def. 2. remember table assignment

but using D(f)(a1) :=0 just creates a function def.

please help me here

suppose we know the following for a function which we donot know

x0 and f(x0)

x0 and f ' (x0) (first derivative at x0)

x1 and f(x1)

x2 and f(x2)

how can we approximate second, third and fourth derivatives of f(x)  for example say at  a point x3

supporse for a function f(x) (which we do knot know), we know

x0  and f(x0)

x1 and f(x1)

x2 and f(x2)

how can we find best approximations for the first , second, third and fourth derivatives?