InterviewSolution
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InterviewSolution
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Find the second - order derivative of : `(i)x^(10)" "(ii)logx" "(iii)tan^(-1)x` |
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Answer» (i) Let `y=x^(10)`. Then, `(dy)/(dx)=10x^(9).` `therefore (d^(2)y)/(dx^(2))=(10xx9)x^(8)=90x^(8)`. Hence, `(d^(2)y)/(dx^(2))(x^(10))=90^(8).` (ii) Let `y=logx.` Then, `(dy)/(dx)=(1)/(x)=x^(-1)`. `therefore (d^(2)y)/(dx^(2))=(d)/(dx)(x^(-1))=(-1)x^((-1)-1)=-x^(-2)=(-1)/(x^(2)).` Hence, `(d^(2))/(dx^(2))(logx)=(-1)/(x^(2)).` (iii) Let `y=tan^(-)x.` Then, `(dy)/(dx)=(1)/((1+x^(2)))=(1+x^(2))^(-1)`. `therefore(d^(2)y)/(dx^(2))=(d)/(dx)(1+x^(2))^(-1)=(-1)(1+x^(2))^(-2).(2x)=(-2x)/((1+x^(2))^(2))`. Hence, `(d^(2))/(dx^(2)){tan^(-1)x}=(-2x)/((1+x^(2))^(2))`. |
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