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Differentiate w.r.t. b
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\frac{a^{2}bbc}{c^{3}a^{4}}
Divide \frac{a^{2}b}{c^{3}} by \frac{a^{4}}{bc} by multiplying \frac{a^{2}b}{c^{3}} by the reciprocal of \frac{a^{4}}{bc}.
\frac{bb}{a^{2}c^{2}}
Cancel out ca^{2} in both numerator and denominator.
\frac{b^{2}}{a^{2}c^{2}}
Multiply b and b to get b^{2}.