Find by implicit differentiation.

Question

Find  by implicit differentiation. ​  ​

Quizplus · Accepted Answer

Taking the derivative of both sides with respect to x using implicit differentiation, we get:
dy/dx = (-2x)/(2y) = -x/y

Multiplying both sides by y, we get:
y(dy/dx) = -x

Substituting the given point (11eac44f_ed8e_cab3_bedf_a9c4d7c5ea44_TB7497_11) for (x,y), we get:
(11eac44f_ed8e_cab3_bedf_a9c4d7c5ea44_TB7497_11)(dy/dx) = -(11eac44f_ed8e_cab3_bedf_a9c4d7c5ea44_TB7497_11)

Simplifying, we get:
dy/dx = -1/y

Substituting y = 11eac44f_ed8e_cab3_bedf_a9c4d7c5ea44_TB7497_11, we get the derivative as:
dy/dx = -1/11eac44f_ed8e_cab3_bedf_a9c4d7c5ea44_TB7497_11

Therefore, the correct choice is D.

Find by Implicit Differentiation. ​ ​

Find by Implicit Differentiation.