InterviewSolution
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InterviewSolution
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If `e^y(x+1)=1,` show that `(d^2y)/(dx^2)=((dy)/(dx))^2.` |
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Answer» We have `e^(y)(x+1)=1 rArre^(y)=(1)/((x+1))" ...(i)"` `rArr y=log{(1)/((x+1))}=log1-log(x+1)` `rArr y=-log (x+1)." ...(ii)"` `therefore(dy)/(dx)=(-1)/((x+1))` `rArr(d^(2)y)/(dx^(2))=(1)/((x+1)^(2))=((dy)/(dx))^(2).` Hence, `(d^(2)y)/(dx^(2))=((dy)/(dx))^(2).` |
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