Differentiate `sin3xcos5x` w.r.t .`x`.

1.	Differentiate `sin3xcos5x` w.r.t .`x`.
Answer» Let `y=sin 3x cos 5x=(1)/(2){2 cos 5x sin 3x}` `=(1)/(2){sin(5x+3x)-sin (5x-3x)}` `=(1)/(2).(sin 8x-sin 2x)=(1)/(2).(d)/(dx)(sin 2x)` `=((1)/(2).8 cos 8x-(1)/(2)xx2 cos2x)=(4 cos 8x -cos2x)`.

Discussion

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If `f(theta) = sin(tan^(-1)(sintheta/sqrt(cos2theta)))`, where `-pi/4 lt theta lt pi/4,` then the value of `d/(d(tantheta)) f(theta)` is