Question
Download Solution PDFयदि \(\rm y=x^{\sec^2x}\times\frac{1}{x^{\tan^2x}}\) है, तो \(\rm \frac{dy}{dx}=?\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
\(\rm y=x^{\sec^2x}\times\frac{1}{x^{\tan^2x}}\)
अवधारणा:
त्रिकोणमितीय सर्वसमिका \(\rm \sec^2x-\tan^2x=1\) का उपयोग कीजिए।
और अवकलज नियम \(\rm \frac{d}{dx}x^n=n x^{n-1}\) उपयोग कीजिए।
गणना:
\(\rm y=x^{\sec^2x}\times\frac{1}{x^{\tan^2x}}\)
\(\rm \implies y=x^{\sec^2x}\times x^{-\tan^2x}\)
\(\rm \implies y=x^{\sec^2x-\tan^2x}\)
\(\rm \implies y=x\)
अब \(\rm x\) के सापेक्ष अवकलज करने पर,
हम प्राप्त करते हैं,
\(\rm \frac{dy}{dx}=1\)
अतः विकल्प (4) सही है।
Last updated on May 26, 2025
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