Question

use the quotient rule to determine the derivative of the function

Answer 1

We are given:

$w(s)=\frac{5+9e^s}{8e^s+7}$

Then:

$w^{\prime}(s)=\frac{(9e^s)(8e^s+7)-(5+9e^s)(8e^s)}{(8e^s+7)^2}\Rightarrow w^{\prime}(s)=\frac{(72e^{2s}+63e^s)-(72e^{2s}+40e^s)}{(112e^s+64e^{2s}+49)}$$\Rightarrow w^{\prime}(s)=\frac{23e^s}{112e^s+64e^{2s}+49}$

***The solution in boold text***

w'(s) = (23e^s) / (112e^s + 64e^(2s)) + 49)