dy/dt is needed from this following equation

Question

Consider x³ + 5xy³ = -1475, find dy/dt when x = 5, y = -4 and dx/dt = 2.

answer should be rounded to 3 decimal places

Answer 1

x³ + 5xy³ = -1475

3x² + 5y³ + 15xy²(dy/dx) = 0

When x = 5 and y = -4, we have 75 - 320 - 1200(dy/dx) = 0

So, dy/dx = 245/1200 = 49/240

Since dy/dx = (dy/dt) / (dx/dt), we get 49/240 = (dy/dt) / 2

So, dy/dt = 98/240 = 49/120