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Differentiate w.r.t. A
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\frac{\mathrm{d}}{\mathrm{d}A}(A^{2}+2)
Multiply A and A to get A^{2}.
2A^{2-1}
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.
2A^{1}
Subtract 1 from 2.
2A
For any term t, t^{1}=t.
A^{2}+2
Multiply A and A to get A^{2}.