Hello, I have a Maths question I cannot get my head around I have tried and tried but no joy I will learn all I can from you please can you help

I have attached the question

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Question 1 and 2:

Differentiate the following functions, simplifying your answers as far as possible. (a) ll?) = H823 (b) 9(a) = :3) (c) 31(2) = 9/4? (d) Ht) 2 sin(sin(sin(t))) (Hint: For part (d), it may help to di'erentiate the function u(t) = sin(sin(t)) rst.) Question 2 10 marks You should be chic to answer this question after studying Uuit 7. Tanya wants to make an aluminium open-topped water tank to collect rain water in her garden. She wants the total capacity of the water tank to be 32 m3. The water tank is a square-based cuboid with its top face removed. It comprises ve faces; a square base of length and width is m, and four vertical wall pieces of height h In. Tanya wants to minimise the total area of aluminium required to build the water tank. &\\\\\\\\\\i hm mm (a) Write down an equation for the total volume of the tank in terms of the height h and width to. Use this equation to express h in terms of in. (b) Show that the total surface area A, in terms of w, is 128 A: 11:2 + w (c) Use differentiation to determine the width in that gives the minimum surface area A of the water tank, and show that this is a minimum. What is the minimum surface area of the water tank? Find the indefinite integral of the function 4x7 - 23 + 4x f (ac) = 2x6 [5] (Hint: it may be helpful to simplify f(x) first.)Use integration by substitution to find the indefinite integral in part (a) and to evaluate (to 2 d.p.) the definite integral in part (b). In part (b), you may use the approximation e ~ 2.71828 in the final evaluation. 328 + 225 (a) dz 29 + 26 [4] (b) et e(e") at [6] 0