How do you differentiate #f(t)= sqrt(( 1+ ln(t) ) / ( 1 - ln(t) ) #?

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Answer 1 · 2018-07-27T20:09:40

#f'(t)=\frac{2}{(1-\lnt)\sqrt{1-(\lnt)^2}}#

Given function:

#f(t)=\sqrt{\frac{1+\ln t}{1-\ln t}}#

#f(t)=\frac{\sqrt{1+\ln t}}{\sqrt{1-\ln t}}#

Differentiating above function w.r.t. #t# using quotient rule as follows

#f'(t)=\frac{\sqrt{1-\ln t}d/dt\sqrt{1+\ln t}-\sqrt{1+\ln t}d/dt\sqrt{1-\ln t}}{(\sqrt{1-\ln t})^2}#

#=\frac{\sqrt{1-\ln t}{1}/{2t\sqrt{1+\ln t}}-\sqrt{1+\ln t}{-1}/{2t\sqrt{1-\ln t}}}{1-\ln t}#

#=\frac{1-\lnt+1+\lnt}{(1-\lnt)\sqrt{1-(\lnt)^2}}#

#=\frac{2}{(1-\lnt)\sqrt{1-(\lnt)^2}}#