In-frame time derivative proof

[yakattack]

Could someone please help with this question.

For non-inertial frames show that the in-frame time derivative D obeys:
D(fa)=fDa+df/dta

Where f is a scalar function and a is a vector.

I know that Df=df/dt and that Da= the sum of the derivatives of the components of a times the relavant basis vector. But can't seem to apply this to prove the question.

 

[marlon]

Well for the non inertial observer, the a vector is a time dependent function. So actually you get $$\vec{a} = a \cdot \vec{e_t}$$. Hence the $$D \vec{a} = a \cdot \frac{d \vec{e_t}}{dt}$$.

marlon