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 both differentiable functions of t and 9x^5y=18.

Answer 1

Begin with function 9x^5y = 18. Take ln both sides or ln(9x^5y) = ln(18). Log rules allow you to bring down the 5y or

5y*ln(9x) = ln(18)

now differentiate implicitly wrt t

d/dt(5y*ln(9x) = ln(18))

5 dy/dt = ln(18)*[-1(ln(9x))^(-2)/x*dx/dt)

You now have all the pieces needed, solve for dx/dt.