Q10 of 26 Page 1

Differentiate with respect to x.

OR


If prove that


To find: derivative



Now,


y = u + v





Taking log both sides:


⇒ log u = log (xsin x)


⇒ log u = sin x log x


{∵ log (ab) = b log a}


Differentiating both sides:












Taking log both sides:


⇒ log v = log (sin x)cos x


⇒ log v = cos x log sin x


{∵ log (ab) = b log a}


Differentiating both sides:













As,




OR


Given: 2 cos (log x) + 3 sin (log x)



Let y = 2 cos (log x) + 3 sin (log x)









Again, differentiating both sides:











{∵ y = 2 cos (log x) + 3 sin (log x)}




Hence Proved


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