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 ) : $\dfrac{x}{\sin^n x}$

Answer 1

Answer:

Step-by-step explanation:

$\dfrac{x}{\sin^n x}$

माना कि   $y=\dfrac{x}{\sin^n x}$

∴ अवकलन करने पर -

$\frac{dy}{dx} =\frac{d}{dx} \dfrac{x}{\sin^n x}\\\\\frac{dy}{dx}=\frac{sin^nx\frac{d}{dx}(x)-x\frac{d}{dx}(sin^nx)}{(sin^nx)^2}\\ \\\frac{dy}{dx}=\frac{sin^nx.1-x.nsin^{n-1}.cosx}{sin^{2n}x}\\\\\frac{dy}{dx}=\frac{sin^{n-1}x(sinx-nxcosx)}{sin^{2n}x}\\\\\frac{dy}{dx}=\frac{sin^{n-1}x(sinx-nxcosx)}{sin^{n+1}x.sin^{n-1}x}\\\\\frac{dy}{dx}=\frac{sinx-nxcosx}{sin^{n+1}x}$

Answer 2

Answer:

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