Final answer:
The constant 'c' is related to integration and is not needed when differentiating a polynomial like t² + 5; the derivative of this function with respect to t is simply 2t.
Step-by-step explanation:
The question 'Why is the c necessary? Find d/dt(t² + 5).' asks about the role of the constant 'c' in the context of differentiation, as well as how to differentiate a specific function with respect to time, t.
When differentiating a function, any constant term becomes zero, as it does not change with t. In the function t² + 5, the '5' is a constant, so when we differentiate with respect to t, it becomes 0. The differentiation of t² using the power rule (where d(t^n)/dt = n*t^(n-1)) results in 2t. Therefore, the derivative of the function with respect to t is
d/dt(t² + 5) = 2t.
The constant 'c' refers to the integration constant that appears when you integrate a function, and it represents any constant value that could have been lost through the differentiation process. However, in the process of finding the derivative, as seen in this example, the constant simply becomes zero and does not play a role in the derivative of a polynomial.