1. find dy/dt if dx/dt = 5 and x = 1 2. Find dx/dt if dy/dt = 3 and y=2

Question

Assume x and y are differentiable equations of t and (9x^5)y=18

Answer 1

9x⁵y = 18; x⁵y = 2; now implicit ly we differentiate: x⁵dy/dt + 5x⁴ydx/dt = 0;

1) dx/dt = 5, x = 12; 12⁵y = 2; y = 2/12⁵; 12⁵dy/dt + 5·12⁴·2/12⁵·5; dy/dt = - 50/12⁶ = - 1.6745·10^-5;

^{2) dy/dt = 3, y = 2; x^5 ·2 = 2; x = 1; 1·3 + 5·1·2dx/dt = 0; dx/dt = - 3/10 ·}