Question

Differentiating a Logarithmic Function In Exercise, find the derivative of the function.

f(x) = In x/(x + 1)^1/2

Answer 1

`(x+2)/(2x^2+2x)`

Explanation:

We are given:
`f(x)=\ln((x)/((x+1)^(1/2)) )`

We will use the Division and Logarithm properties of the Derivative.

`f'(x)=((√(x+1)-x(1)/(2√(x+1)) )/(x+1) )/((x)/(√(x+1)) ) =(x+2)/(2x^2+2x)`