I am having some trouble with these problems

1) If f is aone-to-one function with f(1)=5 and f(1)=4, what is the value of (f¹)^'(5)?

2) Evaluate the derivative of the following function.

f(x)= 4 csc ^-1 (tan e ^x)

d/dx f(x) =

3)A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 2 ft/min. What is the rate in the change of area at the instant that the radius is 12 ft? Type an exact answer in terms of

4)Suppose f is differentiable on (,) and assume it has a local extreme value at the point x=7 where f(7)=0. Let g(x)=xf(x)+3 and let h(x)=xf(x)+x+3 for all values of x.

a. Evaluate g(7), h(7), g(7), and h(7).

b. Does either g or h have a local extreme value at x=7? Explain.