Question

Seja dada a função derivavel

Answer 1

Temos o seguinte:

$y = f(t) = \dfrac{1}{t^3} + \dfrac{t^4}{2} - \dfrac{4}{t^2} = t^{-3} + \dfrac{1}{2} t^4 - 4t^{-2}$

Utilizando $y = t^{n} \therefore \frac{dy}{dt} = n\cdot t ^{n-1}$. Temos a derivada:

$\dfrac{dy}{dt} = \dfrac{d}{dt} \left( t^{-3} + \dfrac{1}{2} t^4 - 4t^{-2} \right ) \\ \\ \\ \dfrac{d}{dt} \left( t^{-3} + \dfrac{1}{2} t^4 - 4t^{-2} \right ) = -3 t^{-4} + 2t^{3} + 8t^{-3} \\ \\ \\ -3 t^{-4} + 2t^{3} + 8t^{-3} = -\dfrac{3}{t^4} + 2t^3 + \dfrac{8}{t^3}$