Just a couple of questions i need some help with:

1. find the first and second derivative of: e^sin(x)

2. A rectangle's lower vertices are on the x-axis and upper vertices on the graph of y = sinx(x) for (0 is less than or equal to x which is less than or equal to pi). Find the expression for the area of the rectangle and the maximum area of the rectangle.

3. for the function cos(x) + sin(x)

a. (i) show that f(-π/4) = 0

(ii) find in terms of pi, the smallest positive value of x which satisfies f(x) = 0.

4. For e^(x)(cosx +sinx) window: -2 < x < 3.

a. find the first derivative

b. the maximum point

c. the second derivative

5. Find the first derivative of (sinxc)^2 cosx

a. show that the maximum point is x = the square root of 1/3

b. find the exact maximum value