InterviewSolution
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InterviewSolution
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If `x^m y^n=(x+y)^(m+n),p rov et h a t(dy)/(dx)=y/xdot` |
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Answer» `"We have "x^(m)y^(n)=(x+y)^(m+n).` Taking log on both sides, we get m log x + n log y = (m+n) log (x+y) Differentiating both sides w.r.t.x, we get `m(1)/(x)+n(1)/(y)(dy)/(dx)=(m+n d)/(x+y dx)(x+y)` `"or "(m)/(x)+(n)/(y)(dy)/(dx)=(m+n)/(x+y)(1+(dy)/(dx))` `"or "{(n)/(y)-(m+n)/(x+y)}(dy)/(dx)=(m+n)/(x+y)-(m)/(x)` `"or "{(nx+ny-my-ny)/(y(x+y))}(dy)/(dx)={(mx+nx-mx-my)/((x+y))}` `"or "(nx-my)/(y(x+y))(dy)/(dx)=(nx-my)/((x+y)x)` `"or "(dy)/(dx)=(y)/(x)` |
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