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Implicit Differentiation - Second Derivative

by nothing123
Tags: derivative, differentiation, implicit
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nothing123
#1
Apr1-06, 10:52 PM
P: 98
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.
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nrqed
#2
Apr1-06, 11:30 PM
Sci Advisor
HW Helper
P: 2,887
Quote Quote by nothing123
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.
nothing123
#3
Apr1-06, 11:50 PM
P: 98
Ahhh, now I see it, thanks for pointing that out!


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