How do you find the derivative of #y= \frac { 7} { 2} ( \frac { 1} { 2} \ln \frac { x + 1} { x - 1} + \arctan x )#?

1 Answer
Cem Sentin
Dec 1, 2017

#y'=-7/(x^4-1)#

Explanation:

#y=7/2*[1/2Ln((x+1)/(x-1))+arctanx]#

=#7/4Ln((x+1)/(x-1))+7/2*arctanx#

=#7/4Ln(x+1)-7/4*Ln(x-1)+7/2*arctanx#

#y'=7/4*1/(x+1)-7/4*1/(x-1)+7/2*1/(x^2+1)#

=#7/2*1/(x^2+1)-7/2*1/(x^2-1)#

=#-7/(x^4-1)#

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