# Find derivatives of the functions defined as follows.y=(te^t=2)/(e^(2t)+1)

Find derivatives of the functions defined as follows. $y=\left(t{e}^{t}=2\right)/\left({e}^{2t}+1\right)$

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$dy/dt=\left(\left({e}^{2t}+1\right)\left(t{e}^{t}+{e}^{t}\right)-\left(t{e}^{t}+2\right)\left(2{e}^{2t}\right)\right)/\left(\left({e}^{2t}+1{\right)}^{2}\right)$
$=\left(\left(1-t\right){e}^{3t}-4{e}^{2t}+\left(1+t\right){e}^{t}\right)/\left(\left({e}^{2t}+1{\right)}^{2}\right)$