Question

If $f\left(x\right)=\underset{a}{\overset{\sin x}{\int }}\log tdt$. Then find $f^{\prime }\left(x\right)$.

Answer 1

Given,

$f\left(x\right)=\underset{a}{\overset{\sin x}{\int }}\log tdt$

Now using Leibnitz's rule use the rule of derivative under integration we get,

$f^{\prime }\left(x\right)=\log \left(\sin x\right).\cos x-\log \left(a\right).0$

or, $f^{\prime }\left(x\right)=\log \left(\sin x\right).\cos x$