H(s) = 1 + √(s \ ) / 1 - √(s) differentiate using quotient rule ​

Question

`h(s) = 1 + √(s \ ) / 1 - √(s)`
differentiate using quotient rule ​

Answer 1

`h^(l) (s) = (1 )/((√(s)) (1-√(s))^(2) )`

Explanation:

Explanation

Given that

`h(s) = (1+√(s) )/(1-√(s) )`

Differentiating equation (i) with respective to 'x' ,we get

`h^(l) (s) =(1-√(s)) (1)/(2√(s) ) -(1+√(s))((-1)/(2√(s) )) )/((1-√(s))^(2) )`

`h^(l) (s) = ((1)/(2√(s) ) -(1)/(2√(s) )X√(s) + (1)/(2√(s) ) +(1)/(2√(s) )X√(s) )/((1-√(s))^(2) )`

`h^(l) (s) = ((2)/(2√(s) ) )/((1-√(s))^(2) )`

`h^(l) (s) = (1 )/((√(s)) (1-√(s))^(2) )`