Final answer:
The derivative of the function s = (8et)/(2et + 1) with respect to time t is found by applying the quotient rule, resulting in 8et/(2et + 1)².
Step-by-step explanation:
To find the derivative of the function s = (8et)/(2et + 1), we will apply the quotient rule of differentiation. The quotient rule states that the derivative of a function that is the quotient of two other functions, u(t) / v(t), is given by (u'v - uv')/v².
In this case, we let u(t) = 8et and v(t) = 2et + 1. Then we find their derivatives u'(t) = 8et and v'(t) = 2et. Applying the quotient rule:
s'(t) =(u'v - uv')/v²
= ((8et)(2et + 1) - (8et)(2et))/(2et + 1)²
= (16et² + 8et - 16et²)/(2et + 1)²
= 8et/(2et + 1)²
Therefore, the derivative of s with respect to t is 8et/(2et + 1)².