Question

In related rates how would you do this
g(x)=(y(x))^3 , (1,3)

Answer 1

the outer function is u^3 and it depends on that value of y(x): dg/dy

y(x) is the next function, and it depends on the value of x: dy/dx

x is the innermost function and drives the whole thing, it is either independant or relies on an external source such as time... dx/dx or dx/dt

since x = 1; y(1) = 3

since y(1) = 3; g(x) = 3^3 = 27

Answer 2

dg/dt = dg/dy* dy/dx* dx/dx (or dx/dt)