Hello I need help on homework, there are 18 questions scattered throughout, I don't need the work, and you don't have to do all of them

. Question 20 . Question 22 Complete the following computation: ((=)) + (() The graph of f (black) and its tangent line (blue) at 1 is given below. Question 24 f(=) = (=)= Find the following using the table below. = P(2) (@) (7:")210 - Ga(=)(10:") Gy(2) P(2) f(I ) 7 6 5 3 Gi(:) - f'(z) -3.5 -7.5 7.5 -6.5 Ga(#) = If h(x) = - 12x . f(x), = P(E) Gi(z) Wi(2)2 - Gz(2) (10:") H() - dh (2)= . Question 17 f(1) = (The product rule is helpful for this problem!) Question 23 d dr sin(I) 1024 Suppose Step 1 d dr sin(1) . f( - 1) = 3 and f'( - 1) = - 9 . g( - 1) = - 1 and g'( - 1) = -5 Step 2 dy (4ed )sin(x) - 4et (sin(z)) 1 d (- sin (z) 10 dr (2 4 ) . h( - 1) = - 10 and h' ( - 1) = - 9. Step 3 4 ar (e* )sin(z) - 4e" (sin(z)) 1 d sin (z) 10 - ( 2- ' ) -5f(x) - 69(I) Step 4 4e sin(z) - 4el cos(I) 1. The derivative of - "at - 1 is equal to 2 h(I) sin (x) 2. The derivative of sin(*( - 5f(x) - 6g(x))) at - 1 is equal to 3. The derivative of tan(of(x))h(x) at - 1 is equal to Question 25 For each step in the above computation, determine the property or properties of the derivative that are used The table below shows values for four differentiable functions. Suppose the following things are true: Step 1 I'(2) = b(=) Constant Rule Difference Rule Quotient Rule B'(z) = (z) Power Rule Constant Multiple Rule Common Derivatives g' (z) - e(z) Sum Rule Product Rule e' (z) = f(z) 0 1 2 3 4 b(z) 3 5 4 1 2 Step 2 1(2) 4 2 5 1 3 e(z) 3 4 1 2 5 Constant Rule Difference Rule Quotient Rule 9(2) 3 4 5 2 1 Power Rule Constant Multiple Rule Common Derivatives Sum Rule Product Rule For the function A(z) = g(z) . b(z) . f(z), evaluate A' (2). Answer: Step For the function B (z) = - 9(z) /(=) . b(z) . evaluate B' (3). Constant Rule Difference Rule Quotient Rule Answer: Power Rule Constant Multiple Rule Common Derivatives Sum Rule Product Rule . Question 29 Question 35 Use the chain rule to find the derivative of y' In(x7) - 5x7 - y' = -9 /(=) = 10v727+ 1026 8 (x ) dy Type your answer without fractional or negative exponents. Use sqrt(x) for v. ('(=) = . Question 37 y-values y-values Differentiate the following function. You do not need to simplify the derivative. h(x) = 4ed hix . Qution 43 h'(=) = Supporte / and f " are differentiable functions. Suppose /( - 7) = - 3 and /"( - ?) = 4. 2 x-values x-values . Question 18 ( )(-3)- If f(x) = 9(z) . h(z), then Differentiate the following function, You do not need to simplify the derivative. A(2) m . Question 40 f' (2 ) - A'(=) = where . Question 31 . Question 33 y sin(6z) + 623 - yl0 = 10 Find the derivative of: Te cos(32). [Hint: use product rule and chain rule!] Use e*x for ". Find the following using the table below. dy (2) 1 4 3 2 Now, find the equation of the tangent line to the curve at z = 0. Write your answer in ma + b format. 1(2) 1 2 4 3 9(2) 4 1 3 2 . Question 39 Y '(2) 3 4 1 2 . Question 34 . " where Use the chain rule to find the derivative of h'(4) if h(z) - f(z) - s(=) Find f(z) = 4(72* - 927) 14 You do not need to expand out your answer. A'(4) if Ma) = 1(z) y el + 2x2 - yl = - 1 s(z) dy h'(4) if A(=) = f((=))