# How do you find #y''# by implicit differentiation of #x^3+y^3=1# ?

##### 1 Answer

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

Let

Then

and since

we have

So we have

From here, the next step is to again differentiate both sides, this time using the quotient rule:

To find

And so:

Finally, recall that

So: