Blog: `g(t) = ln(t)/t^2` Find the derivative of the function.

$\displaystyle{g{{\left({t}\right)}}}=\frac{{\ln{{\left({t}\right)}}}}{{{t}}^{{2}}}$

Find the derivative of the function using the quotient rule.

$g'(t)={t^2[1/t]-ln(t)[2t]}/t^4$

$\displaystyle{g{'}}{\left({t}\right)}=\frac{{{t}-{2}{t}{\ln{{\left({t}\right)}}}}}{{{t}}^{{4}}}$

$\displaystyle{g{'}}{\left({t}\right)}=\frac{{{t}{\left({1}-{2}{\ln{{\left({t}\right)}}}\right)}}}{{{t}}^{{4}}}$

$\displaystyle{g{'}}{\left({t}\right)}=\frac{{{1}-{2}{\ln{{\left({t}\right)}}}}}{{{t}}^{{3}}}$

The derivative of g(t) is $\displaystyle\frac{{{1}-{2}{\ln{{\left({t}\right)}}}}}{{{t}}^{{3}}}.$

$\displaystyle{g{{\left({t}\right)}}}=\frac{{\ln{{\left({t}\right)}}}}{{{t}}^{{2}}}$

Find the derivative of the function using the quotient rule.

$g'(t)={t^2[1/t]-ln(t)[2t]}/t^4$

$\displaystyle{g{'}}{\left({t}\right)}=\frac{{{t}-{2}{t}{\ln{{\left({t}\right)}}}}}{{{t}}^{{4}}}$

$\displaystyle{g{'}}{\left({t}\right)}=\frac{{{t}{\left({1}-{2}{\ln{{\left({t}\right)}}}\right)}}}{{{t}}^{{4}}}$

$\displaystyle{g{'}}{\left({t}\right)}=\frac{{{1}-{2}{\ln{{\left({t}\right)}}}}}{{{t}}^{{3}}}$

The derivative of g(t) is $\displaystyle\frac{{{1}-{2}{\ln{{\left({t}\right)}}}}}{{{t}}^{{3}}}.$

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