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

1 Answer

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

Explanation:

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}}