Question
Download Solution PDFযদি y = log sin x হয়, তাহলে \(\frac{dy}{dx}\) হবে
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFধারণা:
অবকলন শৃঙ্খল নিয়ম বলে যে, যদি y = f(u) এবং u = g(x) উভয়ই অকলনযোগ্য অপেক্ষক হয়, তাহলে:
\(\frac{dy}{dx}=\frac{dy}{du}\times \frac{du}{dx}\)
\(\frac{{d\left( {\ln x} \right)}}{{dx}} = \frac{1}{x},\;for\;x > 0\)
\(\frac{{d\left( {\sin x} \right)}}{{dx}} = \; cosx\)
গণনা:
প্রদত্ত: y = log sinx
ধরি sin x = u
⇒ y = log u
\(\frac{d}{{dx}}\left( {\log u} \right) = \frac{1}{{u}}\frac{d}{{dx}}\left( {u} \right) \)
\(= \frac{1}{{\sin x}}\left( { cos x} \right) \)
সুতরাং, \(\frac{dy}{dx}\) এর মান হবে \(\frac{1}{sin~x} cos~x\)।
Last updated on Jan 11, 2024
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