InterviewSolution
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InterviewSolution
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If `y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/(dx)i s``(-2)/(1+x^2)`for all `x`(b) `(-2)/(1+x^2)`for all `|x|1`(d) none of theseA. `(-2)/(1+x^(2))` for all xB. `(-2)/(1+x^(2))" for all "|x|lt 1`C. `(2)/(1+x^(2))" for "|x|gt1`D. none of these |
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Answer» `y=cos^(-1)((2x)/(1+x^(2)))` `"or "(dy)/(dx)=(1)/(sqrt(1-(4x^(2))/((1+x^(2))^(2))))(d)/(dx)((2x)/(1+x^(2)))` `=-(1+x^(2))/(sqrt((1+x^(2))^(2)))(2(1+x^(2))-4x^(2))/((1+x^(2))^(2))` `=-2(1+x^(2))/(|1-x^(2)|)(1-x^(2))/((1+x^(2))^(2))` `=-2((1-x^(2))/(|1-x^(2)|))((1)/(1+x^(2)))` `={{:((2)/(1+x^(2))",",if |x|gt1),((-2)/(1+x^(2))",",if|x|lt1):}` |
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