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 ) : $\dfrac{\sec x - 1}{\sec x + 1$

Answer 1

Answer:

Step-by-step explanation:

$\frac{secx-1}{secx+1}$

माना  कि  $y=\frac{secx-1}{secx+1}$

$y=\frac{\frac{1}{cosx} -1}{\frac{1}{cosx} +1} =\frac{1-cosx}{1+cosx}$

∴ अवकलन करने पर -

$\frac{dy}{dx} =\frac{d}{dx} [\frac{1-cosx}{1+cosx}]\\\\\frac{dy}{dx}=\frac{(1+cosx)\frac{d}{dx}(1-cosx)-(1-cosx)\frac{d}{dx}(1+cosx)}{(1+cosx)^2}\\\\\frac{dy}{dx}=\frac{(1+cosx)(sinx)-(1-cosx)(-sinx)}{(1+cosx)^2}\\\\\frac{dy}{dx}=\frac{sinx+sinxcosx+sinx-sinxcosx}{(1+cosx)^2}\\\\\frac{dy}{dx}=\frac{2sinx}{(1+cosx)^2}$

Answer 2

Answer:

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