If $$u = {e^{ax}}\sin bx$$ and $$v = {e^{ax}}\cos bx$$, then what is $$u{{du} \over {dx}} + v{{dv} \over {dx}}$$ equal to ?

If $$y = \sin (\ln x)$$, then which one of the following is correct?

If $$y = {\left| {\sin x} \right|^{\left| x \right|}}$$, then what is the value of $${{dy} \over {dx}}$$ at $$x = - {\pi \over 6}$$ ?

What is $${d \over {dx}}\sqrt {1 - \sin 2x} $$ equal to, where $${\pi \over 4} < x < {\pi \over 2}$$ ?