InterviewSolution
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InterviewSolution
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`" If "y=sqrt((1-x)/(1+x))," then "(1=x^(2))(dy)/(dx)` is equal toA. `y^(2)`B. `1//y`C. `-y`D. `-y//x` |
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Answer» `"We have "y=sqrt((1-x)/(1+x)` Differentiating w.r.t. x, we get `(dy)/(dx)=(1)/(2)((1-x)/(1+x))^(1//2-1)(d)/(dx)((1-x)/(1+x))` `=(1)/(2)sqrt((1+x)/(1-x))cdot((1+x)(-1)-(1-x)(1))/((1+x)^(2))` `=-sqrt((1+x)/(1-x))(1)/((1+x)^(2))` `"or "(1-x)^(2)(dy)/(dx)=-sqrt((1+x)/(1-x))(1)/((1+x)^(2))(1-x)^(2)` `"or "(1-x)^(2)(dy)/(dx)=-sqrt((1-x)/(1+x))` `"or "(1-x^(2))(dy)/(dx)=-y` `"or "(1-x^(2))(dy)/(dx)+y=0` |
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