To determine $g'(1)$, we need more information about the function $g(x)$, such as its explicit form. The derivative $g'(x)$ is the rate of change of the function $g(x)$ at any point $x$, and $g'(1)$ refers to the value of the derivative when $x = 1$.

Could you please provide the function $g(x)$, so we can proceed with calculating its derivative and evaluating $g'(1)$?

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Would you like more details on how to find derivatives?

Here are 5 questions that might interest you:

1. How do you find the derivative of a polynomial function?
2. What is the definition of a derivative in calculus?
3. Can you explain the chain rule for finding derivatives?
4. How do you find the second derivative of a function?
5. What are some real-world applications of derivatives?

Tip: When differentiating, pay close attention to rules like the product, quotient, and chain rules depending on the form of the function!