Question
Download Solution PDFयदि y = u2 + log u और u = ex है, तो \(\rm \frac{dy}{dx}\) का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
y = u2 + log u और u = ex
अवधारणा:
शृंखला नियम की अवधारणा का प्रयोग करते हैं,
\(\rm \frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}\)
और \(\rm \frac{d}{dx}e^x=e^x\)
गणना:
\(\rm u=e^x\)
अब, \(\rm x\) के सापेक्ष अवकलन करने पर,
\(\rm \frac{du}{dx}=e^x\)
\(\rm y=u^2+log\ u\)
अब, \(\rm x\) के सापेक्ष अवकलन करने पर,
\(\rm \frac{dy}{dx}=2u \frac{du}{dx}+\frac{1}{u} \frac{du}{dx}\)
अब, \(\rm u \) और \(\frac{du}{dx}\) का मान रखने पर,
\(\rm \frac{dy}{dx}=2e^x\cdot \ e^x+\frac{1}{e^x} \ e^x\)
\(\rm \implies \frac{dy}{dx}=2e^{2x}+1\)
अतः विकल्प (3) सही है।
Last updated on May 26, 2025
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