InterviewSolution
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InterviewSolution
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If `sin(x y)+y/x=x^2-y^2`, find `(dy)/(dx)`. |
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Answer» Given: `sin(xy)+(x)/(y)=x^(2)-y.` Differentiating both sides w.r.t. x, we get `cos(xy).(d)/(dx)(xy)+x.(-(1)/(y^(2)))(dy)/(dx)+(1)/(y).1=2x-(dy)/(dx)` `rArr cos(xy).[x.(dy)/(dx)+y.1]-(x)/(y^(2)).(dy)/(dx)+(1)/(y)=2x-(dy)/(dx)` `rArr[x cos(xy)-(x)/(y^(2)+1)].(dy)/(dx)=2x-(1)/(y)-y cos(xy)` `rArr{xy^(2)cos(xy)-x+y^(2)}.(dy)/(dx)=2xy^(2)-y-y^(3)cos(xy).` Hence, `(dy)/(dx)={(2xy^(2)-y-y^(3)cos(xy))/(xy^(2)cos(xy)-x+y^(2))}.` |
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