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

1 Answer
Eddie
Oct 4, 2016

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

Explanation:

#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 )#

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