I'm stuck on this problem involving implicit differentiation.The instructions ask me to find y ′ , the problem is: ( x − 2 y ) 3 = 2 y 2 − 3So far I've been able to get this far: 3 ( x − 2 y ) 2 ( 1 − 2 y ′ ) = 4 y ( y ′ )I've been trying to manipulate it for a while but I can't figure out how to finish the problem properly.

Question

I&#039;m stuck on this problem involving implicit differentiation.The instructions ask me to find       y    ′  , the problem is:  (  x  −  2  y      )    3    =  2      y    2    −  3So far I&#039;ve been able to get this far:  3  (  x  −  2  y      )    2    (  1  −  2      y    ′    )  =  4  y  (      y    ′    )I&#039;ve been trying to manipulate it for a while but I can&#039;t figure out how to finish the problem properly.

Monica Dennis · Accepted Answer

Another way could be to consider the implicit function  f  =  (  x  −  2  y      )    3    −  2      y    2    +  3  =  0Compute its derivative with respect to   x and   y      f    x    ′    =  3  (  x  −  2  y      )    2        f    y    ′    =  −  6  (  x  −  2  y      )    2    −  4  yNow, use the implicit function theorem            d      y              d      x        =  −            f      x      ′              f      y      ′        =  −            3      (      x      −      2      y              )        2                    −      6      (      x      −      2      y              )        2            −      4      y        =      3    2    ×            (      x      −      2      y              )        2                    3      (      x      −      2      y              )        2            +      2      y

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