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Differentiate w.r.t. A
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\frac{A\times 2\sqrt{220.22}}{\left(\sqrt{220.22}\right)^{2}}
Rationalize the denominator of \frac{A\times 2}{\sqrt{220.22}} by multiplying numerator and denominator by \sqrt{220.22}.
\frac{A\times 2\sqrt{220.22}}{220.22}
The square of \sqrt{220.22} is 220.22.
A\times \frac{100}{11011}\sqrt{220.22}
Divide A\times 2\sqrt{220.22} by 220.22 to get A\times \frac{100}{11011}\sqrt{220.22}.