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.