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Differentiate w.r.t. b
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\frac{a^{2}\times 2b}{b^{3}a}
Divide \frac{a^{2}}{b^{3}} by \frac{a}{2b} by multiplying \frac{a^{2}}{b^{3}} by the reciprocal of \frac{a}{2b}.
\frac{2a}{b^{2}}
Cancel out ab in both numerator and denominator.