How do you find the derivative of $g (t) = \frac{10 {log}_{4} t}{t}$ $g(t)=(10log_4t)/t$ ?

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Answer 1 · 2017-07-21T14:14:13

$\frac{d g}{d t} = \frac{10}{ln 4} \cdot \frac{1 - ln t}{t^{2}}$ $(dg)/(dt)=10/ln4*(1-lnt)/t^2$

What is required is to convert base $4$ $4$ of log to base $e$ $e$ and then use quotient formula

$g (t) = \frac{10 {log}_{4} t}{t}$ $g(t)=(10log_4t)/t$

$= \frac{10 ln t}{ln 4 t}$ $=(10lnt)/(ln4t)$

Hence $\frac{d g}{d t} = \frac{10}{ln 4} \times \frac{t \times \frac{1}{t} - ln t}{t^{2}}$ $(dg)/(dt)=10/ln4xx(txx1/t-lnt)/t^2$

$= \frac{10}{ln 4} \cdot \frac{1 - ln t}{t^{2}}$ $=10/ln4*(1-lnt)/t^2$

How do you find the derivative of g(t)=(10log_4t)/tg(t)=10log4ttg(t)=(10log_4t)/t?