Find the derivative of this function:
g(t)=(8t+10)^2*(10t^2-7)^-3
Using the Chain Rule.
you have
g = u^2 v^-3
so,
g' = 2uv^-3 u' - 3u^2v^-4 v'
= uv^-4 (2vu' - 3uv')
= u/v^4 (2(10t^2-7)(8) - 3(8t+10)(20t))
= -8u/v^4 (40t^2+75t+14)
= -16(4t+5)/(10t^2-7)^4 * (40t^2+75t+14)