Given S = π x ( x + 2 y ) and V = π x 2 y,I'm to show that d S / d x = 2 π ( x − y ) when V is constant, and d V / d x = − π x ( x − y ) when S is constant.I just don't know where to start.

Question

Given   S  =      π    x  (  x  +  2  y  ) and   V  =      π        x    2    y,I&#039;m to show that   d  S      /    d  x  =  2      π    (  x  −  y  ) when   V is constant, and   d  V      /    d  x  =  −      π    x  (  x  −  y  ) when   S is constant.I just don&#039;t know where to start.

plomet6a · Accepted Answer

If   V  =  c then   S  =  π  x  (  x  +            2      c              π              x                  2                      )  =  π      x          2        +            2      c        x  . Hence             d      S              d      x        =  2  π  x  −            2      c              x              2              =  2  π  (  x  −  y  ) You can handle the second question in a similar way.

cimithe4c · Accepted Answer

Hint:  After you use implicit function theorem on the function that is constant, the function that isn&#039;t constant doesn&#039;t refer to a partial derivative - i.e.            d      S              d      x        =            ∂      S              ∂      x        +            ∂      S              ∂      y        ⋅            d      y              d      x      by chain rule.

Given S=pi x(x+2y) and V=pix^2y,I'm to show that dS/dx=2pi(x−y) when V is constant, and dV/dx=−pix(x−y) when S is constant.

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