Question

Encontre as derivadas das funções w=1/t³ + 12t

Answer 1

$w = \dfrac{1}{t^3} + 12t = t^{-3} + 12t\\\\\\w' = \dfrac{dw}{dt} = \dfrac{d}{dt}(t^{-3}+12t) =\dfrac{d}{dt}(t^{-3})+\dfrac{d}{dt}(12t) = \\\\-3t^{(-3-1)}+12 \cdot \dfrac{d}{dt}(t) = -3t^{-4}+12 \cdot 1 = -3t^{-4}+12 = -\dfrac{3}{t^4}+12\\\\\boxed{\boxed{\dfrac{dw}{dt} = -\dfrac{3}{t^4}+12}}$