Final answer:
The derivative of the function g(x) = (e^x) / (4x + 5) is (e^x(4x + 1)) / ((4x + 5)^2).
Step-by-step explanation:
To find the derivative of the function g(x) = (e^x) / (4x + 5), we can use the quotient rule. The quotient rule states that if we have a function in the form of f(x) = u(x) / v(x), then f'(x) = (u'(x)v(x) - u(x)v'(x)) / (v(x))^2. Applying this rule to our function, we have:
g'(x) = ((e^x)(4x + 5) - (e^x)(4)) / ((4x + 5)^2)
Simplifying further, we get:
g'(x) = (e^x(4x + 1)) / ((4x + 5)^2)