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