Final answer:
To find the expression to replace the question mark in the inequality involving the derivative of e^{x^3+4}, we must first calculate the derivative, which using the chain rule is e^{x^3+4} ∙ 3x^2. Without further details, we cannot provide the precise inequality, but it would typically involve comparing this derivative to another function or constant.
Step-by-step explanation:
The original question seems to be missing, but if we use the provided clues and mathematical concepts to deduce what might be asked, we can try to address the missing expression in a differential inequality. It appears that the student is asking about completing the derivative of an exponential function and determining the inequality that would be established.
To make the differential inequality (d)/(dx) e^{x^3+4} >= ? valid, we need to find what expression should replace the question mark. To do this, let's first find the derivative with respect to x:
Let f(x) = e^{x^3+4}, then the derivative of f(x) with respect to x, by the chain rule, is f'(x) = (d)/(dx) e^{x^3+4} = e^{x^3+4} ∙ 3x^2.
Now, if the student needs to establish an inequality, they must be comparing the derivative to some function or constant. Without additional information, we cannot deduce the exact expression, but it should be a function of x or a constant that the derivative of the given expression e^{x^3+4} should be greater than or equal to.