What is the derivative of #1/(1+x^4)#?

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Answer 1 · 2016-08-26T08:52:13

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

#d/dx 1/(1+x^4)#

you might be tempted to use the quotient rule, which is fine but out of personal preference, i would write it as this

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

...and use the power and chain rules

so
#d/dx ( (1+x^4)^(-1) )#

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

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

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