यदि `y=f((2x-1)/(x^(2)+1))` और `f'(x)=sin^(2)x,` तब `(dy)/(dx)` ज्ञात कीजिए

Explanation

दिया गया है-
`y=f((2x-1)/(x^(2)+1))`
दोनों पक्षों का x के सापेक्ष अवकलन करने पर,
`(dy)/(dx)=d/(dx)f((2x-1)/(x^(2)+1))`
`=f'((2x-1)/(X^(2)+1))xxd/(dx)((2x-1)/(x^(2)+1))`
`=f'((2x-1)/(x^(2)+1))xx((x^(2)+1)d/(dx)(2x-1)-(2x-1)d/(dx)(x^(2)+1))/((x^(2)+1)^(2))`
`=f'((2x-1)/(x^(2)+1))xx((x^(2)+1)xx2-(2x-1)xx2x)/((x^(2)+1)^(2))`
`=sin((2x-1)/(x^(2)+1))^(2)xx{((2x^(2)+2)-(4x^(2)-2x))/((x^(2)+1)^(2))}`
`rArr(dy)/(dx)=sin((2x-1)/(x^(2)+1))^(2)xx(-2x^(2)+2x+2)/((x^(2)+1)^(2))`
`rArr(dy)/(dx)=(-2(x^(2)-x-1))/((x^(2)+1)^(2)).sin((2x-1)/(x^(2)+1))^(2)`