Find by implicit differentiation given that .

Question

Find  by implicit differentiation given that  . ​​

Quizplus · Accepted Answer

Implicit differentiation of 11eac44f_ed8e_557c_bedf_2d3d257cc4da_TB7497_11 gives:
d/dx(11eac44f_ed8e_557c_bedf_2d3d257cc4da_TB7497_11) = d/dx(2x^2 + 3xy - y^3 - 1)

Using implicit differentiation, we get: 
22x + 3y - 3y^2(dy/dx) = 0

Solving for dy/dx, we get: 
dy/dx = (22x + 3y) / 3y^2

Substituting x = 11eac44f_ed8e_6f9d_bedf_4c2e4e91d968_TB7497_11 and y = 11eac44f_ed8e_6f9d_bedf_785586a55948_TB7497_11 , we get: 
dy/dx = (22*11eac44f_ed8e_6f9d_bedf_4c2e4e91d968_TB7497_11 + 3*11eac44f_ed8e_6f9d_bedf_785586a55948_TB7497_11) / 3*(11eac44f_ed8e_6f9d_bedf_785586a55948_TB7497_11)^2

Simplifying this gives: 
dy/dx = 11eac44f_ed8e_a39f_bedf_5757216e0f68_TB7497_11

Therefore, the final answer is option C.

Find by Implicit Differentiation Given That