Were assigned questions regarding implicit differentiation and the second derivative but did not receive a formal lesson so I need some explanations. Example: Find the second derivative x^3 + y^3 = 1 I found this solution on the internet and the answer matches the one in the textbook. However, I don't understand how -2xy^3 - 2x^4/y^5 turned into just -2xy^3/y^5 (This is the 5-6 step). Furthermore, I don't see how -2xy^3/y^5 equals -2x(y^3 + x^3)/y^5 (6-7 step). Simply, I need explanations for this solutions rationale. Thanks.
There is an obvious typo in step 5-6...the -2x^4/y^5 term disappears and then reappears on the next line . At the very end they use x^3+y^3=1, which was the initial equation.