How do you differentiate $f(x)= 2 / (e^x + e^-x)^3$ ?

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Answer 1 · 2016-10-04T18:37:39

$= -6 (e^x - e^(-x) )/ ( (e^x + e^-x)^4 )$

$f(x)= 2 / (e^x + e^-x)^3$

$= 2 / (2(cosh x))^3 = 1/4 sech^3 x$

$f'(x) = 3 (1/4) sech^2 x (- sech x) tanh x$

$= -3/4 sech^3 x tanh x$

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

$= -6 (e^x - e^(-x) )/ ( (e^x + e^-x)^4 )$

How do you differentiate f(x)= 2 / (e^x + e^-x)^3f(x)= 2 / (e^x + e^-x)^3?