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