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In my notes I've found a question from the text, 30 in 3.7 that has:

1/2x^-1/2 + 1/2y^-1/2 * y-prime = 0

and in the next step 1/2x^-1/2 becomes x^-1/2 and likewise with y, how is 1/2 canceled out?

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Multiply both sides of the equation by 2. The 1/2 on the left hand side will be cancelled out, and the right hand side will stay the same (since 0 time 1/2 is 0).