Question

Use the quotient rule to determine the derivative of the function

Answer 1

We are given:

`w(s)=(5+9e^s)/(8e^s+7)`

Then:

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

***The solution in boold text***

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