Question

Determine the rate of change equation by implicitly differentiating with respect to

time t.
x^4+ y^4 = 4y

Answer 1

By the power and chain rules, taking derivatives on both sides with respect to
`t` gives

`4x^3 (dx)/(dt) + 4y^3 (dy)/(dt) = 4(dy)/(dt)`

or

`4x^3 (dx)/(dt) + (4y^3-4) (dy)/(dt) = 0`