functions differentation, I believe

Question

Suppose y = (2x-1)^0.5., where x and y are fxns of y.

If dx/dt = 6, find dy/dt when x = 4

Answer 1

dy/dt = dy/dx·dx/dt = 1/2(2x- 1)^-1/2·2·dx/dt = 1/(2x - 1)^1/2·dx/dt. Now at x = 4 dx/dt = 6, so,

dy/dt = 1/(2·4 - 1)^1/2·6 = 6/7^1/2

Answer 2

dy/dt = 0.5(2x-1)^-1/2*(2)

Simplify = 1/(2x-1)^1/2 * dx/dt

Substitute: 1/(2(4)-1)^1/2 * (6)

Answer: 6/(7)^1/2