You are given the following function.g(x) = √7 + 2x(a) Find the derivative of the function using the definition of derivative.g '(x) = (b) State the domain of the function. (If you need to use -∞ or ∞, enter -INFINITY or INFINITY.) , (c) State the domain of its derivative. (If you need to use -∞ or ∞, enter -INFINITY or INFINITY.)

(a) To find the derivative of the function g(x) = √7 + 2x, we first need to rewrite the function in a form that makes it easier to differentiate. We can rewrite √7 as a constant and 2x as 2x^1. So, g(x) = 2x + √7.

The derivative of a constant is 0 and the derivative of x^n is n*x^(n-1). Therefore, the derivative of g(x) is:

g'(x) = d/dx [2x + √7] = 21x^(1-1) + 0 = 2.

(b) The domain of the function g(x) = √7 + 2x is all real numbers, because you can plug any real number into the function and get a real number out. Therefore, the domain is (-INFINITY, INFINITY).

(c) The domain of its derivative, g'(x) = 2, is also all real numbers. This is because the derivative is a constant, and a constant function is defined for all real numbers. Therefore, the domain of the derivative is also (-INFINITY, INFINITY).