Final answer:
The question involves computing derivative expressions for combinations of two functions f and g at x = -4. The calculation depends on having the specific form of the functions, which are not provided. The process involves basic derivative rules such as the product rule, quotient rule, and the chain rule.
Step-by-step explanation:
Based on the given fragments, it appears that the student is asking for the value of different derivative expressions concerning two functions f and g. Without the explicit definitions or expressions for f and g, it isn't possible to provide numerical answers. However, we can explain the process for finding these values:
- To find (fg)′(−4), you would first need the product of functions f and g, then differentiate it, and finally evaluate the derivative at x = -4.
- To find (f/g)'(−4), you need the quotient of f and g, differentiate it using the quotient rule, and then evaluate it at x = -4.
- For (g/f'')(−4), the function g is divided by the second derivative of f, and you need to evaluate this at x = -4 without differentiation.
Each of these operations requires a knowledge of basic calculus principles, such as the product rule, quotient rule, and chain rule for derivatives.