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Question

If y=xa+ax, prove that 2xydydx=xa-ax

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Solution

y=xa+ax=1ax12+ax-12dydx=1a12x-12+a-12x-32LHS = 2xy dydx = 2x 1ax12+ax-121a12x-12+a-12x-32 = 2x12a-12x+12x-a2x2 = 2x12a-a2x2 = xa-ax = RHS Hence, proved.

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