Differentiate `(x)/(sinx)` w.r.t . sinx.

1.	Differentiate `(x)/(sinx)` w.r.t . sinx.
Answer» Correct Answer - `(tan x-x)/(sin^(2)x)` `"Let "u=(x)/(sin x ) and v = sin x` `therefore" "(du)/(dx)=(sin x.(d)/(dx)x -x. (d)/(dx) sin x)/((sin x)^(2))` `=(sin x - x cos x)/(sin^(2)x)" ....(i)"` `"And "(dv)/(dx)=(d)/(dx)( sin x )= cos x" ...(ii)"` `therefore" "(du)/(dv)=(du//dx)/(dv//dx)=((sin x- x cos x)/sin^(2)x)/(cos x )` `=(tan x-x)/(sin^(2)-x)`

Discussion

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