Question

How do you differentiate `x^4+2y^2=8`?

Answer 1

I found: `(dy)/(dx)=-x^3/y`

Explanation:

You use implicit differentiation remembering that `y` is a function of `x`.
So:
`4x^3+4ycolor(red)((dy)/(dx))=0`
`(dy)/(dx)=-cancel(4)x^3/(cancel(4)y)=-x^3/y`