1.

निम्नलिखित फलनों का x के सापेक्ष अवकलन कीजिए- `sqrt(log{sin(x^(2)/3-1)})`

Answer» माना `y=sqrt(log{sin(x^(2)/3-1)})`
दोनों पक्षों का x के सापेक्ष अवकलन करने पर,
`(dy)/(dx)=d/(dx)[sqrt(log{sin(x^(2)/3-1)})]`
`=d/(dx)[log{sin(x^(2)/3-1)}]^(1/2)`
`=1/2(1)/(sqrt(log{sin(x^(2)/3-1)})).d/(dx)log{sin(x^(2)/3-1)}`
`=1/(2sqrt(log{sin(x^(2)/3-1)})).(1)/(sin(x^(2)/3-1))d/(dx)sin(x^(2)/3-1)`
`=1/(2sqrt(log{sin(x^(2)/3-1)}))`
`.(1)/(sin(x^(2)/3-1))cos(x^(2)/3-1).d/(dx)(x^(2)/3-1)`
`=(cot(x^(3)/3-1))/(2sqrt(log{sin(x^(2)/3-1)}))xx((2x)/3)`
`=(xcot(x^(2)/3-1))/(3sqrt(log{sin(x^(2)/3-1)}))`


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