Originally Posted by

**sixstringartist** You're not simply multiplying by y'. y' is a component in the chain rule due to the implicit nature of the problem.

I believe your first problem is incorrect.

$\displaystyle x^3 + y^3 = 25

$

$\displaystyle 3x^2 + 3y^2 (y') = 0

$

Here you are taking the derivative of every term. Because this is implicit, the derivative of y^3 is 3(y)^2 * (y').

Likewise if your problem was:

$\displaystyle

x^3 + \sin{y^2} = 25

$

than,

$\displaystyle

3x^2 + \cos{y^2} * \frac {d(y^2)}{dy} = 0$

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