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प्रश्न
Select the correct answer from the given alternative:
If y = `(5sin x - 2)/(4sin x + 3)`, then `("d"y)/("d"x)` =
पर्याय
`(7 cos x)/(4 sin x + 3)^2`
`(23 cos x)/(4 sin x + 3)^2`
`- (7 cos x)/(4 sin x + 3)^2`
`-(15 cos x)/(4 sin x + 3)^2`
MCQ
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उत्तर
If y = `(5sin x - 2)/(4sin x + 3)`, then `("d"y)/("d"x)` = `underline ((23 cos x)/(4 sin x + 3)^2)`
Explanation:
y = `(5sinx - 2)/(4 sin x + 3)`
Differentiating w.r.t.x, we get
`(dy)/(dx) = ((4sinx + 3)d/dx(5sinx - 2) - (5sinx - 2)d/dx (4sinx + 3))/(4sinx + 3)^2`
= `((4sin x + 3)(5cosx) - (5sinx - 2)(4cos x))/(4 sinx + 3)^2`
= `(20sin x cosx + 15cosx - 20sinxcosx + 8cosx)/(4sinx + 3)^2`
= `(23cosx)/(4sinx + 3)^2`
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