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`(dy)/(dx)` ज्ञात कीजिए : `y=cos^(-1)((1-x^(2))/(1+x^(2))),0 lt x lt 1` |
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Answer» `y=cos^(-1)((1-x^(2))/(1+x^(2)))" "{:("माना "x=tan theta),(rArr theta= tan^(-1)x):}` `rArr" "y=cos^(-1)((1-tan^(2) theta)/(1+tan^(2) theta))` `=cos^(-1)((cos^(2)theta-sin^(2)theta)/(cos^(2) theta+sin^(2) theta))` `=cos^(-1)(cos 2 theta)=2 theta= 2 tan^(-1)x` `rArr" "(dy)/(dx)=2(d)/(dx) tan^(-1)x=(2)/(1+x^(2))` |
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