Final answer:
The derivative of the function using the definition of the derivative is g'(t) = 5.
Step-by-step explanation:
To find the derivative of the function using the definition of the derivative, we need to use the limit definition of the derivative. The derivative of a function g(t) is defined as the limit of the difference quotients as the change in t approaches 0. In this case, we are given four options for the derivative of g(t): a) g'(t) = 5, b) g'(t) = 0, c) g'(t) = 1, d) g'(t) = 6t. We need to determine which option is the correct derivative of the function.
We can start by taking the derivative of each option and see which one matches the function. For example, if we take the derivative of option d, we get g'(t) = 6. However, this does not match the given function.
By comparing the derivatives of options a, b, and c to the given function, we find that option a) g'(t) = 5 is the correct derivative of the function.