यदि है, तो \(\rm \frac{dy}{dx}\) किसके बराबर है?

  1. इनमें से कोई नहीं 

Answer (Detailed Solution Below)

Option 3 :
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संकल्पना:

माना कि हमारे पास दो फलन f(x) और g(x) हैं और वे दोनों अवकलनीय हैं। 

  • श्रृंखला नियम:
  • गुणनफल नियम:
  • log ab = b log a 

गणना:

 , जहाँ a स्थिरांक है। 

दोनों पक्षों में log लेने पर, हमें निम्न प्राप्त होता है

⇒ 

⇒ log xm + log yn = log x + log y + log am+n

⇒ m log x + n log y = log x + log y + (m + n) log a 

x के संबंध में दोनों पक्षों का अवकलन करने पर, हमें निम्न प्राप्त होता है

⇒    [∵   ]  

⇒  

⇒   . 

सही विकल्प 3 है। 

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