# Find the derivative of the following functions (it is to be understood that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are integers): (1 + 1/x)/(1 - 1/x)

**Solution:**

The given function is f(x) = (1 + 1/x)/(1 - 1/x). It can be written as,

f(x) = [ (x+1) /x ] / [ (x-1)/x ] = (x+1) / (x-1)

Using the quotient rule, its derivative is,

d/dx (f(x)) = [ (x-1) d/dx (x+1) - (x+1) d/dx (x-1) ] / (x-1)^{2}

= [ (x-1) (1+0) - (x+1) (1-0) ] / (x-1)^{2} [using the derivative formula, d/dx (x^{n}) = n x^{n-1}]

= [x - 1 - x - 1] / (x-1)^{2}

= -2 / (x-1)^{2}

NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 6

## Find the derivative of the following functions (it is to be understood that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are integers): (1 + 1/x)/(1 - 1/x)

**Summary:**

The derivative of the given function (1 + 1/x)/(1 - 1/x) is -2 / (x-1)^{2}