Question

encontre a derivada da função f(t)=3t²+7 / t²-1

Answer 1

Regra do quociente. 
Vamos achar a derivada do de cima, a derivada do debaixo e aplicar a regra:

$f(t)=\dfrac{u(t)}{v(t)}\\\\\\u(t)=3t^2+7\\\\u'(t)=6t\\\\v(t)=t^2-1\\\\v'(t)=2t\\\\\\f'(t)=\dfrac{u'v-uv'}{(v)^2}\\\\\\f'(t)=\dfrac{6t(t^2-1)-(3t^2+7)(2t)}{(t^2-1)^2}=\dfrac{6t^3-6t-6t^3-14t}{(t^2-1)^2}=\boxed{\dfrac{-20t}{(t^2-1)^2}}$