Differentiate f(x) = sinx * lnx

f(x) = sinx* lnx

To find the
first derivative, we will use the product rule:

Let f(x) =
u*v   such that:

u= sinx   ==>   u' =
cosx

v= lnx  ==>   v' =
1/x

Now we know
that:

if f(x) = u*v    

Them
f'(x) = u'v + uv'

==> f'(x) =  cosx*lnx + sinx*
1/x

==> f'(x) = cosx*lnx +
sinx/x

               =
(x*cosx*lnx + sinx )/x