Find the derivative for each of the following functions. When possible, always simplify the original function first before finding the derivative. 1. Determine the derivative of the following functions. You can use the derivative rules from this section and not find these derivatives by first principles. Simplify first, if necessary, and then find the derivative. a. f(x) = 3x2 - 5x5 + 20x9 + 7 b. g (x) = 2Vx - Vx+ Vx4 - x-3 c. p(x) = 3* - 2ex - sin (2x) + 3 cosx d. m(x) = (3x +2)2 e. s ( t ) = 41 + 51 f. y = 3x2 (4x5 - 2x3) 2. Using the definition of derivative, prove the constant multiplier rule. That is, prove the derivative of g(x) = c f(x) is g'(x) = c f'(x). Follow the same format that was used in the content section to prove the derivative of a constant rule. 3. Determine the equation of the tangent line to the graph of f(x) = -x5 + 3x2 - 2 atx = 1. Confirm the this equation by graphing (DESMOS) both the function, the common point and tangent line. Include a copy of the graphs in your solution. 4. Suggest a function that would have a derivative of f'(x) = 12x2 + 6x - 5. Explain how you arrived at your