How do you find the derivative of #1/(1+x^4)#?

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Answer 1 · 2016-11-16T09:59:35

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

Given function "f(x)" (hypothetical) #rArr1/(1+x^4)lArr# which is a fraction/rational;

#d/dx(f(x))# should be calculated via application of the Quotient Rule of differentiation.

Quotient Rule

#d/dx(f(x))# when #f(x)=a/b# is differentiated into #(d/dx(a)\timesb -a\timesd/dx(b))/b^2#

#(d/dx(1)\times(1+x^4) - d/dx(1/(1+x^4))=1\timesd/dx(1+x^4))/(1+x^4)^2 #

#\rarr ((0)(1+x^4) - 1\times(0+4x^3))/(1+x^4)^2#

#\rarr (0 - 1\times(4x^3))/(1+x^4)^2#

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