1.

`(dy)/(dx)` ज्ञात करें यदि [Find `(dy)/(dx)` if] (i) `y=sec^(-1)((1)/(2x^(2)-1))` (ii) `y=sin^(-1)(2axsqrt(1-a^(2)x^(2)))`

Answer» (i) `x=costheta` रखने पर हमें मिलता है,
`y=sec^(-1)((1)/(2cos^(2)theta-1))=sec^(-1)((1)/(cos2 theta))`
`=sec^(-1)(sec2theta)=2theta=2cos^(-1)x " " [becausex=costheta]`
`therefore(dy)/(dx)=(-2)/(sqrt(1-x^(2)))`
(ii) `ax =sin theta` रखें ताकि `theta=sin^(-1)(ax)`
तो, `y=sin^(-1){2sinthetasqrt((1-sin^(2)theta)}}=sin^(-1)(sin2theta)`
`=2theta=2sin^(-1)(ax)`
`therefore(dy)/(dx)=2(d)/(d(ax))sin^(-1)(ax)*(d)/(dx)(ax)`
`=2(1)/(sqrt(1-a^(2)x^(2)))*a=(2a)/(sqrt(1-a^(2)x^(2)))`


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