1. y = (x^2 + 1)^3 * (x^3 - 1)^2
2. y = (x^3 + 1) / (x^3 - 2)
3. y = x^2 * sqrt(x + 1)
4. find dy/dx and d^2y/dx^2 for x^(1/3) + y^(1/3) = 3 at the point P(1,8)
If you could briefly explain the methods that would be great too. These are the only ones I am stuck on...thanks1
I think Tonio made a small mistake: the derivative for this last one should be
Because this is actually a function, there is no need to differentiate implicitly, as the equation can be rearranged to find y explicitly in terms of y:
Then: . Now just sub in x = 1.
For : . Again sub in x=1.