f (t) = 1/7t^6-5t^4+9t
Well, there's one rule and one property you have to know here. First is the power rule, as described above. Second is the fact that the derivative of x + y is the (derivative of x) + (derivative of y). In other words, differentiate each term separately, then add up all the derivatives at the end. Does this help?
Basically take whatever number that the variable is raised to. Multiply it by whatever constant was there before and then subtract 1 from the power.
So:
$\displaystyle \tfrac{d}{dx}x^2 = 2x$
$\displaystyle \tfrac{d}{dx}2x = 2$
$\displaystyle \tfrac{d}{dx}3x^{5.9} = 3 \cdot 5.9 x^{4.9}$
It's like that.