Please help me with my calculus grade 12 homework this is from the unit derivatives. please ensure that all answers are detailed and hand written.

1. Differentiate. Answers must be fully factored and simplified properly. a)f(x) )cos (2x) b) h(x) = 2e?*cos2x 300e3% sin (3mx) c) h(x) = \f2. Consider functions of the form y = sin (kx), determine all the values of k such that each successive derivative has a lower amplitude that the one before. Show work to justify your answer. (2 marks) 3. True/False: If false, you must correct the question or find a counter example. (6 marks) a) During one cycle of y = 4cos (% x) there will be exactly two different tangents with a slope of 1. b) Another way of expressing In x is nlog, e c) The n'" derivative of y = 2e** will always be 2" k e* d) The 4! derivative of y = asin(kx) is y = k*asin (kx) e) Every successive derivative of y = asin(kx) is sinusoidal. f) The derivative of an exponential function is an exponential function. e?.x 4. Consider the function h(x) = (8 marks total) sin2x a) Compute the properly factored and simplified first derivative. b) Determine the equation of the tangent at x = g c) Using the correct answer to a) determine coordinates of the max/min point with the lowest positive x value, and proving if it is a max or min. 5. Determine any possible functions f and g , where f # g, but such that f is the derivative of g, and g is the derivative of f. If this is not possible, explain why not. The functions cosh(x) and sinh(x) are not part of this course; thus, they are not allowed. [2 marks]