Math, asked by anushripatil20, 9 months ago

derivative of sinx w.r.t.x. cosx is

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Answered by 2fernandesjane

Answer:

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Answered by aryan073

Answer:

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Step-by-step explanation:

$\frac{d}{x} = \frac{ \sin( \alpha ) }{ \cos( \alpha ) }$

$by \: using \: quotient \: rule$

$\frac{d}{dx} = \frac{ \sin( \alpha ) \frac{d}{dx} cos \alpha } { { \cos( \alpha ) } ^{2} } - \cos( \alpha ) \frac{d}{dx} sin \alpha$

$\frac{d}{dx} = \frac{ \cos( \alpha ) \times cos( \alpha ) - cos( \alpha ) \times - \sin( \alpha ) }{ { \cos( \alpha ) }^{2} }$

$\frac{d}{dx} = \frac{ { \cos( \alpha ) }^{2} + \sin( \alpha ) \cos( \alpha ) }{ { \cos( \alpha ) }^{2} }$

$\frac{d}{dx} = \frac{ \cos( \alpha )( \cos( \alpha ) + \sin( \alpha ) ) }{ \cos( \alpha ) \times \cos( \alpha ) }$

cos( alpha) will be cancelled

$\frac{d}{dx} = \frac{ \cos( \alpha ) + \sin( \alpha ) }{ \cos( \alpha ) }$

$is \: the \: answer \: of \: this \: question$

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