Question
Download Solution PDFयदि y = (xx)x है, तो x = 1 पर
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFप्रयुक्त सूत्र:
- log mn = n log m
- खण्डशः अवकलन:
गणना:
दिया गया है कि y = (xx)x,
दोनों पक्षों पर log लेने पर
log y = log (xx)x
सूत्र (1) का प्रयोग करने पर
⇒ log y = x log xx
⇒ log y = x2 log x
x के संबंध में अवकलन करने पर
सूत्र (2) में वर्णित खण्डशः अवकलन करने पर
⇒
चूँकि,
⇒
⇒
उपरोक्त समीकरण में x = 1 रखने पर
⇒
⇒
∴ x = 1 पर
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