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)(x^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 )) } %3D 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 6 = 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. 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)(x^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 )) } %3D 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 6 = 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.