Consider the following. 9X4 -l- y3 = 5X (a) Find y' by implicit differentiation. I y: (b) Solve the equation explicitly for y and differentiate to get y\" in terms of X. I y: (c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a). I y: Consider the following. i= 5" E 4 x (a) Find y' by implicit differentiation. r y: (b) Solve the equation explicitly for y and differentiate to get y' in terms of X. P y: (c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a). r y: 7. [-/1 Points] DETAILS SCALC9 2.6.021. If f( x) + x2[f(x)]5 = 34 and f(1) = 2, find f'(1). f'(1) = Need Help? Read It Watch It 8. [-/1 Points] DETAILS SCALC9 2.6.022. If g(x) + x cos(g(x)) = x, find g'(0). g'(0) = Need Help? Read It10. [I1Points] I DETAILS I SCALC92.6.026. Use implicit differentiation to find an equation of the tangent line to the curve at the given point. HIT tan(X + y) + sec(x y) = 2, (E, E) Need Help? III-un- 11. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCQ 2.6.028. Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y2(6 x) = x3, (2, ~15), (cissoid of Diocles) y:x42x3+\\/? Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y2(y2 - 4) = X2(X2 7), (0, 2) (devil's curve) A graphing calculator is recommended. (a) The curve with equation yz = x3 + 3X2 is called the Tschirnhausen cubic. Find an equation of the tangent line to this curve at the point (1, 2). Q, L y: 4A+4 X (b) At what points does this curve have horizontal tangents? (Order your answers from smallest to largest x, then from smallest to largest y.) (2 xl ( ) (x, y) (x, y) Find y\" by implicit differentiation. X2+xy+y2=6 Need Help? 16. [OH Points] DETAILS PREVIOUS ANSWERS SCALCQ 2.6.040. Find 3/" by implicit differentiation. 2x3 5y3 =9 "0 x: H X