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Differentiate w.r.t. g
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-\frac{1}{2}\times 4g^{-\frac{1}{2}-1}
The derivative of ax^{n} is nax^{n-1}.
-2g^{-\frac{1}{2}-1}
Multiply -\frac{1}{2} times 4.
-2g^{-\frac{3}{2}}
Subtract 1 from -\frac{1}{2}.