Final answer:
Without the specific forms of the functions, we can't calculate the exact derivatives, but we know that the given values like f'(1) = -88/5 represent the slope of the tangent to the graph at x = 1. The derivative is the function's instantaneous rate of change or slope at a particular point. Rules such as the power rule and product rule are used to find derivatives.
Step-by-step explanation:
The student is asking to evaluate the derivative of certain functions at the point x = 1. Although the provided snippets do not give us the explicit forms of these functions, we can discuss the general process of finding a derivative and what the derivative represents.
To find the derivative of a function, we typically use rules of differentiation such as the power rule, the product rule, the quotient rule, or the chain rule. Once we obtain the derivative function, also known as the instantaneous rate of change of the original function, we can substitute the desired point into this new function to get the derivative at that specific point.
For example, if we were given a position function s(t) with respect to time t, the derivative of this position function, denoted as s'(t) or v(t), gives us the velocity function. Further deriving v(t) gives us the acceleration function a(t).
Since the original question about the derivatives at point x = 1 seems straightforward but lacks context, we can't compute the exact derivative without the function's form. However, the values given, such as f'(1) = -88/5, imply that at x = 1, the slope of the tangent to the curve of the function is -88/5. Each of these values represents the slope of the tangent line to the graph of their respective functions at x = 1.