Question
Download Solution PDFx के संबंध में \(\tan^{-1}\left [ \frac{5+x}{1-5x} \right ]\) को अवकलित करें।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
- \(\tan^{-1}a \, +\, \tan^{-1}b=\tan^{-1}\left (\frac{a+b}{1-ab} \right )\) ---- (1)
- da/dx = 0, जहाँ a कोई स्थिरांक है
- \(\frac{d}{dx}\tan^{-1}x=\frac{1}{1+x^2}\) ---- (2)
-
\(\frac{d}{dx}(a+b)=\frac{da}{dx}+\frac{db}{dx}\)
गणना:
\(\frac{d}{dx}\tan^{-1}\left [ \frac{5+x}{1-5x} \right ]\)
\(\Rightarrow \frac{d}{dx}(\tan^{-1}5\, +\, \tan^{-1}x)\) [(1) का उपयोग करने पर]
\(\Rightarrow \frac{d}{dx}(\tan^{-1}5)\, +\, \frac{d}{dx}(\tan^{-1}x)\)
\(\Rightarrow 0+\frac{1}{1+x^2}\) [(2) का उपयोग करने पर]
\(\Rightarrow \frac{1}{1+x^2}\)
Last updated on Jun 20, 2025
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