Final answer:
The derivative of the function g(t) = t - t^(1/7) is g'(t) = 1 - (1/7)t^(-6/7).
Step-by-step explanation:
To find the derivative g'(t) of the function g(t) = t - t1/7, we apply the rules of differentiation to each term individually. For the first term, t, the derivative with respect to t is simply 1, as the power of t is 1.
For the second term, t1/7, the derivative is found by multiplying the exponent by the function and then subtracting 1 from the exponent, according to the power rule. The derivative of t1/7 is therefore (1/7)t(1/7)-1 = (1/7)t-6/7. Combining these, we get:
g'(t) = 1 - (1/7)t-6/7