Calculus
Class 12

Quotient Rule

ddx[f(x)g(x)]=f(ˊx)g(x)f(x)g(ˊx)[g(x)]2\frac{d}{dx}\left[\frac{f(x)}{g(x)}\right] = \frac{f\'(x)g(x) - f(x)g\'(x)}{[g(x)]^2}
123456−0.4−0.3−0.2−0.100.10.2
d/dx[f/g] = (f'g - fg')/g²

Derivative of a quotient. "Low d-high minus high d-low, over low squared."

Real-World Applications

Economics — Rate of change of ratios like GDP per capita.

Finance — Price-to-earnings ratio changes.

Physics — Acceleration in terms of velocity ratios.

Chemistry — Concentration ratio changes.

Biology — Population density rate of change.

Engineering — Efficiency = output/input rate changes.

Sports analytics — Batting average rate changes.

Medicine — Dosage per weight adjustments.

Environmental — Pollution concentration per volume.

Statistics — Rate of change of correlation coefficients.

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