How to differentiate fraction?

Question

how do i differentiate this? first principles not required.

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Answer 1 · 2018-04-21T02:11:46

Chain rule can be used once the fraction is simplified.

Simplify:

#((4x+1)^2)/(sqrt(4x+1))#
#=((4x+1)^2)/((4x+1)^(1/2))#

Exponent Law #a^n / a^m = a^(n-m) #

#=(4x+1)^(2-1/2)#
#=(4x+1)^(3/2)#

Now apply chain rule:

#=(3/2)(4)(4x+1)^(1/2)#
#=6sqrt(4x+1)#