Question

निम्नलिखित फलनों के अवकलन ज्ञात कीजिए (यह समझा जाय कि a, b, c, d,p, q, r और s निशिचत शून्येतर अचर हैं m तथा n पूर्णांक हैंl ) : $\dfrac{4x + 5\sin x}{3x + 7\cos x}$

Answer 1

Answer:

Step-by-step explanation:

$\dfrac{4x + 5\sin x}{3x + 7\cos x}$

माना कि   $y=\dfrac{4x + 5\sin x}{3x + 7\cos x}$

अवकलन करने पर -

$\frac{dy}{dx} =\frac{d}{dx} \dfrac{4x + 5\sin x}{3x + 7\cos x}\\\\\frac{dy}{dx}=\frac{(3x+7cosx)\frac{d}{dx}(4x+5sinx)-(4x+5sinx)\frac{d}{dx}(3x+7cosx)}{(3x+7cosx)^2}\\ \\\frac{dy}{dx}=\frac{(3x+7cosx)(4+5cosx)-(4x+5sinx)(3-7sinx)}{(3+7cosx)^2} \\\\\frac{dy}{dx}=\frac{(12x+15xcosx+28cosx+35cos^2x)-(12x-28xsinx+15sinx-35sin^2x)}{(3x+7cosx)^2}\\ \\\frac{dy}{dx}=\frac{12x+15xcosx+28cosx+35cos^2x-12x+28xsinx-15sinx+35sin^2x}{(3x+7cosx)^2}$

$\frac{dy}{dx}=\frac{15x.cosx+28cosx+28xsinx-15sinx+35}{(3x+7cos)^2}$

Answer 2

Answer:

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