Discuss implicit differentiation with higher-order derivatives. Respond to the following questions.

• Why is implicit differentiation necessary in order to find derivatives of curves which do not represent functions?
• Come up with your own implicitly defined function. What is its first, second, and third derivative?

Find dx2 if 5x3 - y3 = 25. O A. d'y 250r dx2 O B. day 10r(y-x) = da2 ya O c. dy dax2 O D. d'y 10(y3-514) dx2 O E. d'y dax2 = 30x - 6yFind day dx2 if x2y? = 1. O A. 2y O B. Q O C. O D. - O E. - yFind if y = 10 da2 O A. 0 O B. 2y I O C. 20 O D. E . I-2yFind dx2 if 2x3 - 2y* = 50. O A. 6:x2 - 62 O B. O C. 612 O D. 50r O E