Finding the Force Acting on a particle

[LazyMan]

Homework Statement

Given that the velocity of a particle in rectilinear motion varies with the displacement x according to the equation
x* = bx^-3

where b is a positive constant, find the force acting on the particle as a function of x.

Homework Equations

Hint: F = mx** = mx* dx*/dx

Note: All the x's have dots on top of them representing with respect to time. I used * here instead.

The Attempt at a Solution

I used the hint and solved for the derivative of bx^-3 and got -3bx^-4. I put this back into the hint equation and ended up getting
-3b²m all divided by x⁷

Is this correct? I think I am doing something wrong.

 

[jambaugh]

Remember you are taking a time derivative so you must use the chain rule:

x'(t) = f(x)
x"(t) = f'(x) x'
(where x' = dx/dt)
(Which the hint equation is giving you.)
It looks like you are doing it right.