Derivatives and Velocity in Dynamical Magnetism - Solving a Physics Problem

[moo5003]

Alright, I'm doing a dynamical magnetism problem for my physics class. I've got it almost done except I need to take the derivative of 1/x^3 with respect to time. X in this case is a variable for meters, I want to turn this into an expression with velocity (Velocity is given) but I'm not sure what that is.

d(1/x^3)/dt = ? I'm pretty sure its not just 1/v^3 but that would be nice ^_^. Any help would be appreciated.

Would this just be -4x^-3*v?

 

[Curious3141]

Alright, I'm doing a dynamical magnetism problem for my physics class. I've got it almost done except I need to take the derivative of 1/x^3 with respect to time. X in this case is a variable for meters, I want to turn this into an expression with velocity (Velocity is given) but I'm not sure what that is.

d(1/x^3)/dt = ? I'm pretty sure its not just 1/v^3 but that would be nice ^_^. Any help would be appreciated.

Would this just be -4x^-3*v?

No, you differentiated wrongly. What is \frac{d}{dx}(x^{-3}) ?

Then \frac{d}{dt}(x^{-3}) = \frac{d}{dx}(x^{-3})(\frac{dx}{dt}) = v\frac{d}{dx}(x^{-3}) as you correctly surmised.

 

[moo5003]

No, you differentiated wrongly. What is \frac{d}{dx}(x^{-3}) ?

Then \frac{d}{dt}(x^{-3}) = \frac{d}{dx}(x^{-3})(\frac{dx}{dt}) = v\frac{d}{dx}(x^{-3}) as you correctly surmised.

k, I guess I have a bigger problem then originally thought since X is not given :/.

 

[Curious3141]

k, I guess I have a bigger problem then originally thought since X is not given :/.

What ?

x is a variable denoting displacement right ? And don't mix up the cases - stick to small x.

All I'm saying is you differentiated wrong.

What is \frac{d}{dx}(x^n) ? This should be in the textbook. Now plug in n = -3.