Implicit Differentiation - Second Derivative

1. nothing123

97
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.

Last edited: Apr 1, 2006
2. nrqed

3,048
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.

3. nothing123

97
Ahhh, now I see it, thanks for pointing that out!