Final answer:
To find dy/dt for the function y = t² − 2, differentiate each term separately using the power rule. Since the derivative of t² is 2t and the derivative of a constant is 0, the correct derivative dy/dt is 2t.
"the correct option is approximately option B"
Step-by-step explanation:
The question asks us to find the derivative of y with respect to t, that is, dy/dt, given that y = t² − 2. To find dy/dt, we need to use differentiation, which is a tool in calculus for finding the rate at which a function is changing at any given point. Using the power rule of differentiation, we differentiate each term of the function separately. In this case, the derivative of t² is 2t (since the power rule states that d/dt of t to the power of n is n times t to the power of n-1) and the derivative of a constant is 0. Therefore, the derivative of y with respect to t is:
dy/dt = d/dt (t²) - d/dt (2)
Applying the power rule:
dy/dt = 2t - 0
Hence, dy/dt equals 2t. Option b) correctly represents the derivative of y with respect to t.