#### Answer

$f'(t) = -14t^{-2}-48t^{-5}$

#### Work Step by Step

In order to derivate this function you have to apply the power rule:
$\dfrac{d}{dx}(x^n)=nx^{n-1}$
But first let's rewrite the function
$f(t) = 14t^{-1}+12t^{-4}+\sqrt{2}$
then:
$f'(t) = 14(-1)t^{-2}+12(-4)t^{-5}$
$f'(t) = -14t^{-2}-48t^{-5}$