1)Find f '(x) for f(x) = cos (3x³) (Show working)

2) Find f '(x) for f(x) = ln(x³+ e^4x)(Show working)

3) Find dy/dxby implicit differentiation for x + y = xy (Show working)

4)Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 6x^(1/3)+ 3x^(4/3). You must justify your answer using an analysis of f '(x) and f "(x)

5)What is the maximum volume in cubic inches of an open box to be made from a 16-inch by 30-inch piece of cardboard by cutting out squares of equal sides from the four corners and bending up the sides? Your work must include a statement of the function and its derivative. Give one decimal place in your final answer. (Show working)