यदि y = sin (log cos x) तो \(\rm \frac{dy}{dx}\) का मूल्य क्या है?

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  1. cos (log (cos x)).tan x
  2. sin (log (cos x)).tan x
  3. -cos (log (cos x)).tan x
  4. -cos (log (sin x)).tan x

Answer (Detailed Solution Below)

Option 3 : -cos (log (cos x)).tan x
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Detailed Solution

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अवधारणा:

अवकलन सूत्र

\(\rm \frac{d\: (sin x)}{dx}\) = cos x 

\(\rm \frac{d\: (log \: x)}{dx} = \frac{1}{x}\)

\(\rm \frac{d\: (cos\: x)}{dx} \) = - sin x

त्रिकोणमिति सूत्र

\(\rm tan\: \theta = \frac{sin \: \theta }{cos\: \theta }\)

 

गणना:

दिया हुआ: y = sin (log cos x)

x के संबंध में अवकलन

\(\rm \frac{dy}{dx}\) = \(\rm \frac{d\;\left \{sin\: (log (cos \:x )) \right \} }{dx}\)

= cos (log (cos x)). \(\rm \frac{d\;\left \{ (log (cos\: x )) \right \} }{dx}\)

= cos (log (cos x)). \(\rm \frac{1}{cos\: x}\) \(\)\(\frac{d\: (cos \:x)}{dx}\)

= cos (log (cos x)). \(\rm \frac{1}{cos\: x}\) .(- sin x)

= - cos (log (cos x)). \(\rm \frac{sin\: x }{cos\: x}\)

= - cos (log (cos x)).tan x

\(\rm \frac{dy}{dx}\) = - cos (log (cos x)).tan x

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