Question
Download Solution PDFयदि y = tan (cot−1 x) तो \(\frac{{{\rm{dy}}}}{{{\rm{dx}}}}\) at x = 1 किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFधारणा:
\({\cot ^{ - 1}}{\rm{x}} = {\rm{\;}}{\tan ^{ - 1}}\left( {\frac{1}{{\rm{x}}}} \right)\)
tan (tan-1 x) = x
गणना:
दिया हुआ:
y = tan (cot−1 x)
\( \Rightarrow {\rm{y}} = \tan \left[ {{{\tan }^{ - 1}}\left( {\frac{1}{{\rm{x}}}} \right)} \right]\)
⇒ y = 1/x (∵tan (tan-1 x) = x)
x के संबंध में अवकलन करके हमें मिलता है
\(\frac{{{\rm{dy}}}}{{{\rm{dx}}}} = {\rm{\;}} - \frac{1}{{{{\rm{x}}^2}}}\)
x = 1 पर
\(\frac{{{\rm{dy}}}}{{{\rm{dx}}}} = \; - \frac{1}{1} = \; - 1\)
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