Find the derivative of the function using logarithmic differentiation

[longman3]

Could you help my solve the following example:

 

a(t)=(1+r^2)^3 (1-t^2)^4 sin^3 t

 

Many Thanks

[studiot]

Is this coursework?

In which case it belongs in homework help.

 

What happens if you take the log of both sides of your equation and then differentiate each side?

[Unity+]

Could you help my solve the following example:

 

a(t)=(1+r^2)^3 (1-t^2)^4 sin^3 t

 

Many Thanks

You are taking the derivative in regards to which variable? If so, is r the constant or simply another variable? We need more information.

[andrewcellini]

You are taking the derivative in regards to which variable? If so, is r the constant or simply another variable? We need more information.

i presume the op meant to put another t there (t and r are just so close together lol), and thus the derivative is wrt t.

Edited May 8, 2015 by andrewcellini

[imatfaal]

It is just a very tedious but plain derivative iff r should be t . I would love to see a quick route - but you could just multiply the bugger out and then differentiate; no dramas just a lot of algebra.

 

If r is not t - then presuming A is not dependent on r - and given the A(t) I think that can be assumed then it is even easier