Final answer:
The derivative of 2.5t^4 * 5t^2 - 96a is 10t^4.
Step-by-step explanation:
The derivative of a function can be found using the power rule, which states that the derivative of x^n is n*x^(n-1). In this case, the given function is 2.5t^4 * 5t^2 - 96a. To find the derivative, you need to differentiate each term of the function with respect to t.
Derivative of 2.5t^4 = 4 * 2.5 * t^(4-1) = 10t^3
Derivative of 5t^2 = 2 * 5 * t^(2-1) = 10t
Derivative of -96a = 0 (since 'a' is a constant)
Combining these derivatives, the derivative of the given function is 10t^3 * 10t - 0 = 10t^4