Logarithmic differentiation Take the logarithm of both sides of the following equation. Then apply the rules...
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Logarithmic differentiation Take the logarithm of both sides of the following equation. Then apply the rules for logarithms to simplify the right-han side. x3 e4x y !! x² +1 { y = [ (x^3 e^(4x) )/ (sqrt)Xx^2 + 1))] } Then take the derivative (implicitly) and solve for dy/dx. QUESTION 18 inverse trigonometric function Find the derivative dy/dx y = In (t2 + 4) - (1/2) arctan (t/2) QUESTION 19 4 points Save inverse trigonometric derivative Derivative of Inverse -- Inverse Trigonometric inv trig w/ chain rule a) Find the derivative f(x) by applying the chain rule and the derivatives of inverse trigonometric functions, where f(x) cos (arcsin (3/ x)) = { f(x) = cos ( arcsin ( 3/x)) } !3! b) Redo this derivative by first simplifying to eliminate the trigonometric and inverse trigonometric functions (leaving only a ratio of side lengths, described using the variable x). [ Substitute e = arcsin (3/x) sin e = 3/x and use this to draw the right triangle for the angle e] Show the two derivatives are equivalent. QUESTION 20 optimization on interval I. Find all the critical points for each of the following functions ex/3 a. f(x) x² +9 f(x) = [ (e^\(x/3) / (x^2+9) ] ) b. g(x) = 3 - 15 - 2x| g(x) = .3 - |5 - 2x|. II. Find the maximum and the minimum of the function on the given interval. Evaluate the function at all critical points in the interval, as well as the endpoints. ex/3 on the interval (0,5] a. f(x) x2 +9 f(x) = [ (e^\(x/3) / (x^2+9) ] ) b. g(x) - 3 - 15 - 2x| on the interval (1,6) g(x) = .3 - |5 - 2x|. Logarithmic differentiation Take the logarithm of both sides of the following equation. Then apply the rules for logarithms to simplify the right-han side. x3 e4x y !! x² +1 { y = [ (x^3 e^(4x) )/ (sqrt)Xx^2 + 1))] } Then take the derivative (implicitly) and solve for dy/dx. QUESTION 18 inverse trigonometric function Find the derivative dy/dx y = In (t2 + 4) - (1/2) arctan (t/2) QUESTION 19 4 points Save inverse trigonometric derivative Derivative of Inverse -- Inverse Trigonometric inv trig w/ chain rule a) Find the derivative f(x) by applying the chain rule and the derivatives of inverse trigonometric functions, where f(x) cos (arcsin (3/ x)) = { f(x) = cos ( arcsin ( 3/x)) } !3! b) Redo this derivative by first simplifying to eliminate the trigonometric and inverse trigonometric functions (leaving only a ratio of side lengths, described using the variable x). [ Substitute e = arcsin (3/x) sin e = 3/x and use this to draw the right triangle for the angle e] Show the two derivatives are equivalent. QUESTION 20 optimization on interval I. Find all the critical points for each of the following functions ex/3 a. f(x) x² +9 f(x) = [ (e^\(x/3) / (x^2+9) ] ) b. g(x) = 3 - 15 - 2x| g(x) = .3 - |5 - 2x|. II. Find the maximum and the minimum of the function on the given interval. Evaluate the function at all critical points in the interval, as well as the endpoints. ex/3 on the interval (0,5] a. f(x) x2 +9 f(x) = [ (e^\(x/3) / (x^2+9) ] ) b. g(x) - 3 - 15 - 2x| on the interval (1,6) g(x) = .3 - |5 - 2x|.
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Fundamentals of Materials Science and Engineering An Integrated Approach
ISBN: 978-1118061602
4th Edition
Authors: David G. Rethwisch
Posted Date:
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