# Thread: Finding another Derivative

1. ## Finding another Derivative

The theory of relativity predicts that an object whose mass is z when it is at rest will appear heavier when moving at speeds near the speed of light. When the object is moving at speed v, its mass m is given by the following equation, where c is the speed of light.
m=z/sqrt(1-v^2/c^2)

(a) Find dm / dv.

(b) In terms of physics, what does dm / dv tell you?

2. Got it!!!
(a) (vz)/(c^2sqrt(1-v^2/c^2)^3)

I made it m=z(1-v^2/c^2)^(-1/2)
then to find the derivative i used the chain rule
(-1/2)z(1-v^2/c^2)^(-3/2)((2v(c^2))/(c^4))
bring the (1-v^2/c^2)^(-3/2) to the denominator and it simplifies to: (vz)/(c^2sqrt(1-v^2/c^2)^3)
That really doesnt look like it makes sense because it is so hard to read but i get it

(b) the rate of change of mass with respect to the speed