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. a) y = x3 + cosx b) p(x) = 2ex - 1/2 sin(2x) +3 c) s t = 413 + 514 d) y = 3x2(4x3 - 2x) 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. Use Winplot/Desmos to graph f(x) = 4x - 5x2 + 2x. Use the slider to find the tangent at various points. Plot these points and verify that the derivative (found using the sum and difference rule) goes through all these points. 4. Suggest a function that would have a derivative of f'(x) = 12x2 + 4x - 10. Explain how you arrived at your