Question

please wrote out all steps NEATLY, thank you in advance

dy Use implicit differentiation to find dx 3y2 2x-5 2x + 5 dy dx =

Answer 1

Solution 3y2 = 2x-5 2x+5 y as y(x) Differentiate both sides of the equation with respect to x d (3y2) = (2+5) (3y?) = 3. (y) Apply the chain rule: df(u) dx die de f = u?, u=y = 3 (1²) d (y) = 6y. (y) di (2+3) Apply the Quotient Rule : (:)' = " (2x–5)(2x+5)-(2x+5)(2x–5) (2x+5)

2(2x+5)-2(2x-5) (2x+5) 20 20 (2x+5) 6y (y) = (2x+5) For convenience, write do (y) as y byy' = (275 Divide both sides by 6y Oyy 20 (2x+5) 6y бу y 10 3y (2x+5) Write y' as d (y) di (y) = 3y(2x+5) 10 10 dy dx 3y (2x+5)