Question

find the derivative of log(tan5x​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

$Here , y=log(tan5x)$

$Differential \: with \: respect \: to \: x$

$\frac{dy}{dx}=\frac{d}{dx}log(tan5x)$

$\frac{dy}{dx}=\frac{1}{tan5x}*\frac{d}{dx}(tan5x)$

$\frac{dy}{dx}=\frac{1}{tan5x}*Sec²5x*\frac{d}{dx}(5x)$

$\frac{dy}{dx}=\frac{Sec²5x}{tan5x}*5$

$\frac{dy}{dx}=\frac{5Sec²5x}{tan5x}$

$\frac{dy}{dx}=5(Sec²5x*Cot5x)$

$\frac{dy}{dx}=5(\frac{1}{Cos²5x}*\frac{Cos5x}{Sin5x})$

$\frac{dy}{dx}=5(\frac{1}{Cos5x*Sin5x})$

$\frac{dy}{dx}=5(\frac{2}{2Sin5x*Cos5x})$

$\frac{dy}{dx}=5(\frac{2}{Sin10x})$

$\frac{dy}{dx}=\frac{10}{Sin10x}$

$\frac{dy}{dx}=10Cosec10x$