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  • Choose the correct answer out of 4 options given against each Question If y=(1+1/x^2 )/(1-1/x^2 ) then dy/dx is

Choose the correct answer out of 4 options given against each Question

If y=\frac{1+\frac{1}{x^{2}}}{1-\frac{1}{x^{2}}}  then \frac{dy}{dx}  is

A.\frac{-4x}{\left(x^{2}-1\right)^{2}}

B.\frac {-4 x}{x^{2}-1}

C.\frac{1-x^{2}}{4 x}

D.\frac{4 x}{x^{2}-1}

Answers (1)

\\y=\frac{1+\frac{1}{x^{2}}}{1-\frac{1}{x^{2}}}=\frac{x^{2}+1}{x^{2}-1} \\ \\ \frac{dy}{dx}=\frac{ \left( x^{2}-1 \right) \left( 2x \right) - \left( x^{2}+1 \right) \left( 2x \right) }{ \left( x^{2}-1 \right) ^{2}}=\frac{ \left( 2x \right) \left( x^{2}-1-x^{2}-1 \right) }{ \left( x^{2}-1 \right) ^{2}}=-\frac{4x}{ \left( x^{2}-1 \right) ^{2}} \\ \\

Hence, the answer is option A

Posted by

infoexpert21

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