How do you find #y''# by implicit differentiation of #x^3+y^3=1# ?
Differentiate one step at a time, then when you have a
Implicit differentiation is remarkably similar to "regular" differentiation. We just need to treat any term with a y in it slightly differently.
First, we differentiate both sides of the equation:
By the addition rule:
We know that
Now we use the chain rule to implicitly find
So we have
From here, the next step is to again differentiate both sides, this time using the quotient rule:
Finally, recall that
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