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यदि `y=sin^(-1)((2^(x+1))/(1+4^(x)))`, हो,तो `(dy)/(dx)` ज्ञात कीजिए।

Answer» `y=sin^(-1)((2^(x+1))/(1+4^(x)))`
`y=sin^(-1)((2^(x).2)/(1+4^(x)))`
`y=sin^(-1)((2.2^(x))/(1+(2^(x))^(2)))`
माना `2^(x)=tantheta`, तब `theta=tan^(-1)(2^(x))`
`thereforey=sin^(-1)[(2tantheta)/(1+tan^(2)theta)]`
`rArry=sin^(-1)(sin2theta)`
`rArry=2theta=2tan^(-1)2^(x)`
`therefore(dy)/(dx)=d/(dx)(2tan^(-1)2^(x))`
`rArr(dy)/(dx)=2xx1/(1+(2^(x))^(2)).d/(dx)(2^(x))`
`rArr(dy)/(dx)=2/(1+4^(x)).2^(x)log_(e)2`
`rArr(dy)/(dx)=(2^(x+1)(log_(e)2))/(1+4^(x))`


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