If f (x) = In (2x + 1) , then its third derivative is f () (x) =Let f and g be differentiable functions. Which of the following is/are correct statements of the product rule for derivatives? O (f(x)g(z) )' = f(z)g(z) + f(x)g (1) O (f(g(z)) )' = f'(g(=))g'(2) O (f(x)g(z) )' = f(z)g' (1) O let u = f(x) and v = g(x) then (wv)' = u'v + uv' O (f(x)g(z) )' = f(z)9 (z) + f(x)g(I) d d (f(z)g(z)) = g(z)-f(x) + f(1) -9(z)Let f and g be differentiable functions. Which of the following is/are correct statements of the chain rule for derivatives? (f(x) g(z) )' = f'(g(z))g'(z)g(z) O Let u = g(x) then A f(u) = du d f(u) du let u = f(x) and v = g(x) then (uv)' = uut uv' A f(g(z)) = f'(g(z) )g'(1) O (f(g(2)))' = f'(z)g'(1) O (f (g(=) ) )' = f' (z)g(z) + f(z)g'(z)The goal of this question is to emphasize how our differentiation rules can be used even when it seems like you might not have enough information to answer the question. Set P(I) = (1+ 4)f(x) + rg(I) where f and g are differentiable functions. Use the rules of differentiation to write a formula for p' (x) on paper. Then: Suppose that we are further told that f(-4) = 5, f'(-4) = 3, g(-4) = 4 and g'(-4) = 2. Using this information and the formula that you have deduced for p' (x), find p'(-4)- Answer : p (-4) = NumberSuppose that h(x) = f(g(x)). a) Which of the following formulas for the derivative of h(x) is correct? Oh'(z) = f'(g(x))g'(z) O h'(z) = f(g'(z))g'(z) Oh'(z) = f'(g'(1)) Oh'(z) = f'(g(I)) b) Given the following table of information of the values of functions at different values of z, evaluate h' (2) and h' (4). Function T =-4 I = 2 I = 3 1 =4 h(I) -1 -5 -3 6 g(I) 5 -4 0 3 f(I) 3 4 6 g'(1) 2 7 -4 f' (I) 4 5 2 8 Answer: h (2) = Answer: h (4) =Find an equation of the tangent line to the curve y = (4x +2)er at the point : = 0. Answer. FORMATTING: Your answer should be an equation of the form y = me + b.Find life equation of the tangent line to the curve 4 y=5l(:|:431) at the point [115] . {Hint simplify before differentiating.) Your answer must be an equation ofthe form 3.. = mg.- + b. This question accepts equations. E_g_ y-2 = Six-4H1. Help | Switch to Equation Editor | F're'u'ieu.I Consider the following function f() = (x +51 +7)e] Find the x-coordinate(s) of the point(s) where the tangent line to the graph of f is horizontal. Answer. FORMATTING: If there is more than one point, separate these & values with a semi-colon