Differentiation!!!!!!!!!!!!!!!!!!!!!!!

Question

f(x)=ln(√((x-1)^3/(x+1))

Answer 1

The derivative of the fuction

Using  the identity 

Using  the identity 

Differentiate the sum term by term and factor out constant

Using  the identity 

Using the chain rule

Where u = x -1 and 

Differentiate the sum term by term

The derivative of  -1 is zero and x is 1

Using the chain rule

Where u = x+1and 

Differentiate the sum term by term

The derivative of 1 is zero and  x is 1

The solution is

Answer 2

Given that

Simplify the given equation by using identity log(a^b)=bloga

For our constants

Simplify this with the identity log(a/b)=loga-logb

Differtiate the sum terms by terms and factor out constants

Simplify log(x-1)^3 in the form of loga^b = bloga

Factor out constants

Using chain rule

Differentiate the sum terms by terms

Derivative of -1 is 0

Simplify the expression

The derivative of x is 1

 

Using chain rule

Therefore the diffrentiation of given equation is