Question
Download Solution PDFयदि फलन f, x = c पर अवकलनीय है और c के कुछ प्रतिवेश में एकैकी हैं, तथा g, f का व्युत्क्रम फलन है, तो g'{f(c)} का मान ज्ञात कीजिये?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
यदि g, f का व्युत्क्रम फलन है तो gof(x) = g(f(x)) = x
अवकलन का श्रृंखला नियम: [g(f(x))]' = g'(f(x)).f '(x)
गणना:
दिया गया है, फलन f, x = c पर अवकलनीय है और c के किसी प्रतिवेश में एकैकी है, g, f का व्युत्क्रम फलन है।
⇒ g(f(x)) = x
दोनों पक्षों को x के सापेक्ष अवकलित करने पर,
⇒ g'(f(x)).f '(x) = 1
⇒ g'(f(x)) = \(\rm \frac{1}{f'(x)}\)
अतः, x = c पर,
g'(f(c)) = \(\rm \frac{1}{f'(c)}\)
∴ सही विकल्प (1) है।
Last updated on Jun 18, 2025
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