Question

differentiate the following wrtx x^3logx-cotx
please help​

Answer 1

$\orange{\bold{\underline{\underline{solution : - }}}}$

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$Let y= \: \cot 3[log(x {}^{3} )]</p><p></p><p>$

$\red{\bold{{differentiating \: w. \: r. \: t.x \: we \: get \: \frac{dy}{dx} }}}$

$\red{\bold{{ = \: \frac{d}{dx} }}} [ \cot( log( {x}^{3} ) ]$

$\purple{\bold{{ = \: 3[ \cot( log( {x}^{3} ) ] {2}^{} \: \frac{d}{dx} }}}[ \cot( log( {x}^{3} ) ]$

$\purple{\bold{{ = \: 3 \cot2)[ log( \frac{x}{3} ) ] }}}. \: - \cos {}^{2} log( {x}^{3} ) ]. \: \frac{d}{dx} \: log \: {x}^{3}$

$\orange{\bold{{ = - 9 \cos {}^{2})[ log( {x}^{3} )]. \cot^{2}[ log( {x}^{3} ) ] \: x }}}$

$\bold{{ = - 3 \cot {}^2 [ log( {x}^{3} )] . \cos {}^{2} [ log \: x {3} ].3 \frac{d}{dx } (logx) }}$

$\bold{{ = - 3 \cot{}^{2}}}[ log( {x}^{3} )]. \cos \: 2[ log( {x}^{3} ] .3 \times \frac{1}{ \times }$

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