Question
Download Solution PDFयदि x = t2 और y = t3 तो \(\rm \frac{d^2y}{dx^2}\) = ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
अवकलजों का श्रृंखला नियम: x के दो फलनों u और v के लिए हमारे पास है: \(\rm \frac{du}{dv}=\frac{du}{dx}\times\frac{dx}{dv}\)
गणना:
हमारे पास x = t2 और y = t3 हैं।
⇒ \(\rm \frac{dx}{dt}\) = 2t और \(\rm \frac{dy}{dt}\) = 3t2
अवकलजों के श्रृंखला नियम का उपयोग करके हमारे पास है:
\(\rm \frac{dy}{dx}=\frac{dy}{dt}\times\frac{dt}{dx}\)
= \(\rm 3t^2\times\frac{1}{2t}\)
= \(\rm \frac{3t}{2}\)
अब, \(\rm \frac{d^2y}{dx^2}\) = \(\rm \frac{d}{dx}\left(\frac{dy}{dx}\right)\)
= \(\rm \frac{d}{dx}\left(\frac{3t}{2}\right)\)
= \(\rm \frac{3}{2}\left(\frac{dt}{dx}\right)\)
= \(\rm \frac{3}{2}\left(\frac{1}{2t}\right)\)
= \(\rm \frac{3}{4t}\)
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