How would I work these ? Can you give explanation please

1. Candace tried to find the derivative of the function y = h(x)e-4() but her group members disagreed with her result. What did she get right? What did she get wrong? Correct her work. y' = h' (x)e-4 (2) + h(I)e-45(2) ( -4) After figuring out her error, Candace attempted to check her solution by rearranging the right side of the equation y = h(x)e-4f(@) into a fraction and using the quotient rule to differentiate. Verify the correct solution using this method. 2. Two students are trying to find the derivative y' of y = e() . Otto tried using the chain rule, letting the interior function be u = h (z) K(x) . . Naomi tried using the chain rule, letting the interior function be u = Are Otto's and Naomi's methods both acceptable? Try both methods. 3. During Exam 2, some students forgot the formula for the quotient rule. However, Alexander was able to figure it out again using other derivative rules and techniques. Find the quotient rule formula using the method he came up with below. Alexander rewrote (f(2) "(2) ) as a product (f(x) . (9(x)) -1 )' to derive the quotient rule. 4. Derive a formula for a f (g(h(x)) ) . Use your formula to find a [ (tan 4x) ]2. Check your solution by finding the derivative using an alternative method. 5. Find y' if y = V 2274 two different ways. 6. Confirm your solutions to problems 1, 2, 3, 5 above using logarithmic differentiation. 7. A group of three students is trying to find the derivative y' of y = In (f(x)g(x)). . Karl suggests using the chain rule and letting the interior function be u = f(x)g(x). . Suvra suggests using an algebraic log property to rewrite the right side of the equation, then differentiating. . Kimshi suggests applying a base e to both sides of the equation, simplifying, then using implicit differentiation to find the derivative. Are these three methods acceptable? Try them. Justify your answer. 8. Find y' if y = In ( sin(cos r) ) using four different methods. Does the formula found in problem 4 apply here? If so, it may be used as one of the methods