Calculus Answers

what is the derivaties of the following functions :
1- y = 4 / x-5 Inx
2- y = e^-x + e^x / e^x +1
3- y = e^ (1 - In x)
4- y = 6 In ( x^ 1/2 - 3 x)

A manger wants to install a rectangular notice board, ABCD, with area 1600cm^2, in the office meeting room. The notice board is to be subdivided by two thin strips of red tape AC and PQ, where PQ is parallel to AB, the shorter side of the rectangle. The length of red tape is to be a minimum. Determine the dimmensions of the notice board.

Determine all functions satisfying the functional relation :

f(x) + f(1/1-x) = 2(1-2x)/x(1-x)

What is the integration of x [sup]2[/sup]e[sup] x 2[/sup]?

1- f(x) = 2x3 - 6x + 3
2- f(x) = -5x2+5x+8
3- f(x) = 4/ x2 +4x+8
4- f(x) =(x2 + 9)1/2

for the above find the critical points and intervals on which the function is increasing and decreasing then identify the local extreme values of the function , if any saying where they are taken on ?

‎6[sup]x-1[/sup] =3[sup]2x[/sup]

Find the derivative of y to respect of x if y=e[sup]-8x[/sup] is.

Use polar coordinate to find the volume of solid inside the cylinder and inside the ellipsoid.

Find the maximum and minimum values of the function f(x,y) = x2 ‐2y subject to the constraint
that x2 + y2 = 9 and please show calculations