InterviewSolution
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InterviewSolution
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यदि (If) `y=tan^(-1)((sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))))` , (find) `(dy)/(dx)` ज्ञात करें |
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Answer» यहाँ `y=tan^(-1)[(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))]` `x^(2)=costheta` रखने पर, `y=tan^(-1)[(sqrt(1+costheta)-sqrt(1-costheta))/(sqrt(1+costheta)+sqrt(1-costheta))]=tan^(-1)[(sqrt(2)"cos"(theta)/(2)-sqrt(2)"sin"(theta)/(2))/(sqrt(2)"cos"(theta)/(2)+sqrt(2) "sin"(theta)/(2))]` `=tan^(-1)[(1-"tan"(theta)/(2))/(1+"tan"(theta)/(2))]=tan^(-1)[tan((pi)/(4)-(theta)/(2))]` `=(pi)/(4)-(theta)/(2)=(pi)/(4)-(1)/(2)"cos"^(-1)x^(2)` x के सापेक्ष अवकलित करने पर हमें मिलता है, `(dy)/(dx)=0-(1)/(2)*(d)/(dx)(cos^(-1)x^(2))` `=-(1)/(2)*(-1)/(sqrt(1-(x^(2))^(2)))*(d)/(dx)(x^(2))=(1)/(2)*(1)/(sqrt(1-x^(4)))*2x=(x)/(sqrt(1-x^(4)))` |
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