Math, asked by nagathanabhi, 5 months ago

if y = 5 sin x -2/ 4 sin x -3 then ,dy/dx is

Answers

Answered by mathdude500
18

\large\underline\blue{\bold{Given \:  Question :-  }}

\bf \:  If \: y  = \dfrac{5sinx \:  - 2}{4sinx - 3} , \: then \: find \: \dfrac{dy}{dx}

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\bf \:\huge \red{AηsωeR} ✍

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\large\underline\blue{\bold{Given :-  }}

\bf \:  y  = \dfrac{5sinx \:  - 2}{4sinx - 3}

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\large\underline\blue{\bold{To \:  Find :-  }}

\bf \:  \dfrac{dy}{dx}

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\begin{gathered}\Large{\bold{\pink{\underline{Formula \:  Used \::}}}}  \end{gathered}

\bf \:  ⟼ 1. \:  \boxed{\bf \:  \dfrac{d}{dx}sinx = cosx}

\bf \:  ⟼ 2. \:  \boxed{\bf \:  \dfrac{d}{dx}cosx =  -  \: sinx}

\bf \:  ⟼ 3. \:  \boxed{\bf \:  \dfrac{d}{dx}k = 0}

\bf \:  ⟼ 4. \:  \boxed{\bf \:  \dfrac{d}{dx}\dfrac{u}{v}  = \dfrac{v\dfrac{d}{dx}u \:  -  \: u\dfrac{d}{dx}v}{ {v}^{2} } }

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\large\underline\purple{\bold{Solution :-  }}

\bf \:  ⟼ y  = \dfrac{5sinx \:  - 2}{4sinx - 3}

Differentiate both sides w. r. t. x, we get

\bf \:  ⟼ \dfrac{d}{dx}y = \dfrac{d}{dx} \bigg(\dfrac{5sinx \:  - 2}{4sinx - 3} \bigg)

\bf \: \dfrac{dy}{dx}= \dfrac{(4sinx - 3)\dfrac{d}{dx}(5sinx - 2) - (5sinx - 2)\dfrac{d}{dx}(4sinx - 3)}{ {(4sinx - 3)}^{2} }

\bf \:  ⟼ \dfrac{dy}{dx} = \dfrac{(4sinx - 3)(5cosx - 0) - (5sinx - 2)(4cosx - 0)}{ {(4sinx - 3)}^{2} }

\bf \:  ⟼ \dfrac{dy}{dx} = \dfrac{ \cancel{20sinxcosx} - 15cosx -  \cancel{20sinx \: cosx} \:  + 8cosx}{ {(4sinx \:  - 3)}^{2} }

\bf \:  ⟼ \dfrac{dy}{dx} = \dfrac{ - 7cosx }{ {(4sinx \:  - 3)}^{2} }

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Answered by arpita278
0

Answer:

use the formula:

(ad-bc) f'(x)/(cf(x)+d)^2

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