यदि `y=xsin x,` तब dy/dx का मान ज्ञात कीजिएः।सिद्ध करे की `(1)/(y) (dy)/(dx)-(1)/(x)=cot x`

Explanation

`y=x sin x Rightarrow (dy)/(dx)=(d)/(dx)(x sin x)=x(d)/(dx)(sin x)+sin x(d)/(dx)(x)`
`Rightarrow (dy)/(dx)=x cos x+sin x`
`Rightarrow (1)/(y)(dy)/(dx)=(x cos x+sin x)/(y)=(x cos x+sin x)/(x sin x)`
`=cot x+(1)/(x)`