higher derivative and quotient rule Let f(x) be given by the following sin x f(x) =...

 

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higher derivative and quotient rule Let f(x) be given by the following sin x f(x) = { f(x) = [ (sin x) / (x)] Find the first three derivatives, f'(x), f'(x), and f"(x). QUESTION 2 chain rule - multi layer Apply the chain rule to find the derivative of the following funciton f(x). Since there are multiple layers of composition, the chain rule will have to be applied multiple times. f(x) = [esin Vx + 1]° QUESTION 3 Apply the chain rule and other rules of differentiation to find the derivative of each of the following functions. x2 а. f(x) = x sin x² + 1 { f(x) = x sin [ (x^2) /(x^2+1)] g(x): b. ex cos x { g(x) = e^(x cos x) %3D QUESTION 4 Implicit derivative Find the equation of tangent line at the point (3,1) for the function defined implicitly by the following equation 2(x2 + y?)² = 25(x² – !! { 2(x^2 + y^2)^2 = 25(x^2 - y^2) } %3D higher derivative and quotient rule Let f(x) be given by the following sin x f(x) = { f(x) = [ (sin x) / (x)] Find the first three derivatives, f'(x), f'(x), and f"(x). QUESTION 2 chain rule - multi layer Apply the chain rule to find the derivative of the following funciton f(x). Since there are multiple layers of composition, the chain rule will have to be applied multiple times. f(x) = [esin Vx + 1]° QUESTION 3 Apply the chain rule and other rules of differentiation to find the derivative of each of the following functions. x2 а. f(x) = x sin x² + 1 { f(x) = x sin [ (x^2) /(x^2+1)] g(x): b. ex cos x { g(x) = e^(x cos x) %3D QUESTION 4 Implicit derivative Find the equation of tangent line at the point (3,1) for the function defined implicitly by the following equation 2(x2 + y?)² = 25(x² – !! { 2(x^2 + y^2)^2 = 25(x^2 - y^2) } %3D