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Differentiate w.r.t. c
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\frac{-b^{2}c\times 9a^{2}}{3a\times 2bc^{2}}
Multiply -\frac{b^{2}c}{3a} times \frac{9a^{2}}{2bc^{2}} by multiplying numerator times numerator and denominator times denominator.
\frac{-3ab}{2c}
Cancel out 3abc in both numerator and denominator.