Question
Download Solution PDFx2 के संबंध में 2x sin x2 का अवकलन कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
प्राचलिक रूप:
यदि f(x) और g(x), x में फलन हैं, तो
\(\rm df(x)\over dg(x)\) = \(\rm \frac{df(x)\over dx}{dg(x)\over dx}\)
गणना:
माना कि f(x) = 2x sin x2 और g(x) = x2 है।
\(\rm \frac{df(x)}{dx}\) = 2 sin x2 + 2x cos x2 (2x)
\(\rm \frac{df(x)}{dx}\) = 2 sin x2 + 4x2 cos x2
साथ ही
\(\rm \frac{dg(x)}{dx}\) = 2x
अब g(x) के संबंध में f(x) का अवकलन करने पर
\(\rm df(x)\over dg(x)\) = \(\rm \frac{df(x)\over dx}{dg(x)\over dx}\)
\(\rm df(x)\over dg(x)\) = \(\rm \frac{2 \sin x^2 + 4x^2 \cos x^2 }{2x}\)
\(\rm df(x)\over dg(x)\) = \(\rm {\sin x^2\over x} + 2x \cos x^2 \)Last updated on Jul 11, 2025
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