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Differentiate w.r.t. c
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\frac{2a^{2}b\times 8c^{3}}{3c\times 3abc}
Divide \frac{2a^{2}b}{3c} by \frac{3abc}{8c^{3}} by multiplying \frac{2a^{2}b}{3c} by the reciprocal of \frac{3abc}{8c^{3}}.
\frac{2\times 8ac}{3\times 3}
Cancel out abcc in both numerator and denominator.
\frac{16ac}{3\times 3}
Multiply 2 and 8 to get 16.
\frac{16ac}{9}
Multiply 3 and 3 to get 9.