Find dx/dy by implicit differentiation x^2=x+y/x−y

Question

Find dx/dy by implicit differentiation x^2=x+y/x−y

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Verity 2 days 2021-07-21T22:11:20+00:00 1 Answers 0 views 0

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    2021-07-21T22:12:31+00:00

    Answer:

    { \tt{ \frac{dy}{dx} ( {x}^{2}) =  \frac{dy}{dx}  ( \frac{x + y}{x - y}) }} \\ { \tt{2x =  \frac{(x - y) \frac{dy}{dx}   + (x + y) \frac{dy}{dx} }{ {(x - y)}^{2} } }} \\ { \tt{ \frac{dy}{dx}(2x) = 2x {(x - y)}^{2}  }} \\ { \tt{ \frac{dy}{dx} =  {(x - y)}^{2}  }}

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )