Step 1 Recall that the derivative of a constant times a differentiable function is equal to the constant times the derivative of the function. In other words, we have the following where c is a constant. [cf(x ) ] = Co F( x )] Applying this rule when finding the derivative of the given function gives us the following result. f' (t ) = =[9(t - 9)5 ] = at 7-9)5 (17 - 9) Step 2 Recall the general power rule, which states that if the function fis differentiable and h(x) = [f(x)]", where n is a real number, then the following is true. h' ( x ) = -" [f(x ) ]" = n[f(x )in - if' (x) For -[(t - 9)"] we have a differentiable function being raised to a power. Let g(t) = t - 9 and n = 5. Therefore, we have the following. " [(g(t))"] = [(t] - 9) 5 ] Applying the general power rule to the above gives us the following result. [(g(t))"] = nig(t)]" - 1g'(t) - [(t - 9)5] = 5(t7 - 9)5- 1/ +5(t 7 - 9)4