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

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

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

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

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