1. Find the first derivative of: 4 . Consider the problem of estimating a root of the equation i) f(x) = x2e3x ; ii) g(x) = cosh(sin(x)) . cos(2x) - x =0 via the Newton's method. 2. Use the definition for cosh A and prove that for all A, Beginning with initial guess X, = IT/8 , apply two iterations to 2cosh"(A) = 1+cosh(2A) . estimate a root to 3 decimal places. Show all of your working 3. The volume V of a sphere with surface area S is given by and state x, and x2. V 6VIT Calculate the rate at which the volume of a sphere is increasing when its surface area is 100mm and is increasing at a rate of 1 mm2/s