Geometrically, there is a close relationship between the plots of {{MATH_7}} and {{MATH_8}}, they are reflections of each other over the line {{MATH_9}}: {{CMD_10}} {{ENV_11}} {{COMMENT_12}} {{COMMENT_13}} {{COMMENT_14}} {{CMD_15}} One may suspect that we can use the fact that {{MATH_16}}, to deduce the derivative of {{MATH_17}}. We will use implicit differentiation to exploit this relationship computationally.