Question

A derivada da equação fazendo o MMC entre 1 e $t^{2}$ .

$S(t)=t^{2} +\frac{1}{t^{2}}$

Answer 1

$S(t)=t^2+\frac{1}{t^2}\\\\S(t)=\frac{t^2*t^2+1}{t^2}\\\\S(t)=\frac{t^4+1}{t^2}$

Aplicando a regra do quociente, temos:

$S'(t)=\frac{(t^4-1)'*t^2-(t^4-1)*(t^2)'}{(t^2)^2}\\\\S'(t)=\frac{4t^3*t^2-(t^4-1)*2t}{t^4}\\\\S'(t)=\frac{4t^5-2t^5+2t}{t^4}\\\\S'(t)=\frac{2t^5+2t}{t^4}\\\\S'(t)=\frac{t*(2t^4+2)}{t^4}\\\\\boxed{S'(t)=\frac{2t^4-2}{t^3}=2t-\frac{2}{t^3}}$