How do we differentiate ?,

Question

#x##/##x##+##1#

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Answer 1 · 2017-05-16T15:18:44

To differentiate #1/(x+1)# use the quotient rule. To differentiate #x/x+1# simplify first.

Derivative of a constant
#d/dx(x/x+1) = d/dx(1+1) = d/dx(2) = 0# #" "# (for #x != 0#)

Quotient Rule

#d/dx(u/v) = (u'v-uv')/v^2#

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