Help needed doing differentiation (quotient rule)

[lavster]

Hi, can someone help me solve this double derivative please:

$$\frac{1}{c}\frac{d^2}{dt^2}\frac{1}{c^2t^2-x^2-y^2-z^2}$$ I am assuming you get use the quotient rule but I am getting so many terms I am getting confused... Its in my notes and I am not quite getting it...

Thanks

 

[disregardthat]

It's a matter of scrutinizing your every step. If you know the quotient rule you should be able to do this with enough time.

 

[lavster]

Its trying to prove that two sides are equal ( this is left hand side of wave equation). I am getting two different answers and assumed it was something to do with this as it was so long...

 

[HallsofIvy]

The first derivative of
$$(c^2t^2- x^2- y^2- z^2)^{1/2}$$
with respect to t (assuming x, y, and z are independent variables and not functions of t) is $$(1/2)(c^2t^2- x^2- y^2- z^2)^{-1/2}(2c^2t)= c^2t(c^2t^2- x^2- y^2- z^2)^{-1/2}$$
and it is not that difficult to differentiate again.

If x, y, and z are functions of t, yes, that is going to be difficult!