Question #4cfca

2 Answers
Soumalya Pramanik
Jun 1, 2017

#1/x^2#

Explanation:

#d/dx (x-1)/x#
#= {x * d/dx (x-1) - (x-1) * d/dx x}/{x^2}# [Division Rule of Differentiation]
#= {x * (d/dx x - d/dx 1) - (x - 1) * 1}/{x^2}# [Subtraction Rule ; #d/dx x = 1#]
#= {x * 1 - x + 1}/(x^2)# [#d/dx constant = 0#]
#= (x - x + 1)/(x^2)#
#= 1/x^2#

Ratnaker Mehta
Jun 1, 2017

# 1/x^2.#

Explanation:

#d/dx{(x-1)/x},#

#=d/dx{x/x-1/x},#

#=d/dx{1-x^-1},#

#=d/dx(1)-d/dx(x^-1),#

#=0-(-1*x^(-1-1)),#

#=x^-2,#

#=1/x^2.#

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