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

$4x^3 \dfrac{dx}{dt} + 4y^3 \dfrac{dy}{dt} = 4\dfrac{dy}{dt}$

or

$4x^3 \dfrac{dx}{dt} + (4y^3-4) \dfrac{dy}{dt} = 0$