For the implicitly-dened function, calculate the derivative with respect to x. 2 5 x+s=+ x S (Use symbolic notation and fractions where needed.) Calculate the derivative of y with respect to x when sin(x + y) = 4x + 2 cos(y). (Use symbolic notation and fractions where needed.) Calculate the derivative of y with respect to x. Express derivative in terms of x and y. e3\" = sin (3,74) (Express numbers in exact form. Use symbolic notation and fractions where needed.) 3 yell\" ' 3xy 4yZ cos[y4) 3x9 Incorrect Find the derivative of the function y = 2 sin_1 (4x). (Use symbolic notation and fractions where needed.) ' i\" a: II 173: Find the derivative of the function y = 5 tan'1 (T ). (Use symbolic notation and fractions where needed.) Compute the derivative of the function y = 7 cos_1 (x4). (Use symbolic notation and fractions where needed.) Calculate the derivative. 2+x) _ l ytan (236 (Express numbers in exact form. Use symbolic notation and fractions where needed.) Find an equation of the tangent line to the curve at the given point. xy + x2}!2 = 20, (4,1) (Express numbers in exact form. Use symbolic notation and fractions where needed. Let y = f (x) and give the equation in terms of y and x.) equation of the tangent line: The curve x' + y' = 3xy was first discussed in 1638 by the French philosopher-mathematician Rene Descartes, who called it the folium (meaning "leaf"). Descartes's scientific colleague Gilles de Roberval called it the jasmine flower. Both men believed incorrectly that the leaf shape in the first quadrant was repeated in each quadrant, giving the appearance of petals of a flower. Find an equation of the tangent line at the point (27 9 ) 28 ' 28 2 X 2 -2+ (Express numbers in exact form. Use symbolic notation and fractions where needed. Let y = f(x) and give the equation in terms of y and x.) equation of the tangent line:Assuming x and y are functions of a variable I, use implicit differentiation to relate dy Differentiate the equation 7x y = 1 with respect to the variable t and express in terms of d". aft (Use symbolic notation and fractions where needed.) amidx. d! d1 d1