Final answer:
The correct answer to the student's question is 'Partial Derivatives', as it pertains to differentiating functions with three variables in the context of calculus.
Step-by-step explanation:
The student is asking about the method for differentiating functions of multiple variables, specifically within the context of calculus. When dealing with functions involving three variables, the most appropriate method to find the rate of change or differentials is through the use of partial derivatives. This is because partial derivatives allow you to take the derivative with respect to one variable while holding the others constant.
For example, considering the effect of calculus operations on dimensions, when you calculate the derivative of a function like velocity with respect to time, you're finding the rate of change of velocity, which is acceleration. In multivariable calculus, when you have a function of three variables and need to find the gradient or rate of change in each dimension separately, you would use partial derivatives.
Furthermore, Equation 3.7 and the concept of exponential derivatives indicate that there are various techniques that can be employed when differentiating, some of which might use the chain rule or exponential functions to find the rate of change of functions that are more complex.
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