# What is the second derivative of the function #f(x) = (x) / (x - 1)#?

##### 1 Answer

#### Explanation:

For this problem, we will use the quotient rule:

We can also make it a little easier by dividing to get

**First derivative:**

#= (d/dx1)+(d/dx((x-1)(d/dx1)-1(d/dx(x-1)))/(x-1)^2)#

#=0+((x-1)(0)-(1)(1))/(x-1)^2#

#= -1/(x-1)^2#

**Second derivative:**

The second derivative is the derivative of the first derivative.

#=-((x-1)^2(d/dx1)-1(d/dx(x-1)^2))/[(x-1)^2]^2#

#=-((x-1)^2(0)-1(2(x-1)))/(x-1)^4#

#=2/(x-1)^3#

We could also have used the power rule

#= -(x-2)^(-2)#

#=2(x-2)^(-3)#

which is the same as the result we obtained above.