1. Use the limit definition of the derivative to find f' (x). f (x) = x2 - 3x 2). Find the derivatives of the following functions. a) f(x) = 7x5 + 8x b) f(x) = 27x3-9x*+3x3 3x 3) Use the product rule or the quotient rule to differentiate the following functions. a) f(x) = (1+)(x2+ 1) x4 - 1 b) f (x) =- x2+14) Calculate the following derivatives. a) f(x) = 5x2 + cos x b) f (x) = sinx + 3e3x 5) A stone thrown vertically. Suppose a stone is thrown vertically upward from the edge of a cliff with an initial velocity of 64 ft/s from a height of 32 ft above the ground. The height s (in feet) of the stone above the ground t seconds after it is thrown is s = -16tz + 64t + 32. a) Determine the velocity v of the stone after t seconds. b) When does the stone reach its highest point? c) What is the height of the stone at the highest point